Annales Fennici Mathematici
type: channel
description: Annales Fennici Mathematici was founded in 1941 by P.J. Myrberg under the name Annales Academiæ Scientiarum Fennicæ Series A. I. Mathematica. The journal was owned and published by Academia Scientiarum Fennica until 2021 when the Finnish Mathematical Society took over as the owner. Annales Fennici Mathematici publishes original research papers in all fields of mathematics. Historically the emphasis has been on analysis. One volume, divided into two issues, is published annually.
publisher: The Finnish Mathematical Society
language: en
publication name: Annales Fennici Mathematici
issn: 2737-0690
items: Revisiting cyclic elements in growth spaces
items: On \(L^p \to L^q\) infinitesimal relative boundedness of Schrödinger operators \((-\Delta)^{\alpha/2}+v\)
items: A step towards the tensorization of Sobolev spaces
items: A variant of inverse mean curvature flow for star-shaped hypersurfaces evolving in a cone
items: Anisotropic weighted Levin–Cochran–Lee type inequalities on homogeneous Lie groups
items: Directional pliability, Whitney extension, and Lusin approximation for curves in Carnot groups
items: Limits of manifolds with a Kato bound on the Ricci curvature. II
items: Generalized Schwarzians and normal families
items: Off-diagonal matrix extrapolation for Muckenhoupt bases
items: Carathéodory convergence and the conformal type problem
items: Greedy matching in optimal transport with concave cost
items: Matrix-weighted bounds in variable Lebesgue spaces
items: A dual simple proof of the classical Bernstein and Calabi–Bernstein theorems
items: Sharp Fourier decay estimates for measures supported on the well-approximable numbers
items: Exceptional set estimates in finite fields
items: Two footnotes to the F. & M. Riesz theorem
items: On bounded energy of convolution of fractal measures
items: Covering sponges with tubes
items: Conformal and holomorphic barycenters in hyperbolic balls
items: A counting formula for extreme contractions on regular polygonal Banach spaces
items: A deterministic proof of Loewner energy reversibility via local reversals
items: Finite dimensionality of Besov spaces and potential-theoretic decomposition of metric spaces
items: The Stepanov theorem for Q-valued functions
items: Normalized solutions for logarithmic Schrödinger equation with a perturbation of power law nonlinearity
items: Unique extremality of affine maps on plane domains
items: On the sharp second order Caffarelli–Kohn–Nirenberg inequality
items: Logarithmic vanishing theorems on weakly 1-complete Kähler manifolds
items: A clustering theorem in fractional Sobolev spaces
items: CMC hypersurfaces with polynomial volume growth in warped products and the nonexistence of entire solutions to the minimal hypersurface equation
items: The Landau–Bloch type theorems for certain class of holomorphic and pluriharmonic mappings in C^n

Revisiting cyclic elements in growth spaces
type: item
description: We revisit the problem of characterizing cyclic elements for the shift operator in a broad class of radial growth spaces of holomorphic functions on the unit disk, focusing on functions of finite Nevanlinna characteristic. We provide results in the range of Dini regular weights, and in the regime of logarithmic integral divergence. Our proofs are largely constructive and allow for substantial simplifications of earlier works that previously relied on the Carleson Corona Theorem, such as the Korenblum–Roberts Theorem, as well as a more recent result of El-Fallah, Kellay and Seip.
subject: Articles
  topic: section
subject: Singular inner functions
  topic: keywords
subject: cyclic vectors
  topic: keywords
subject: shift operator
  topic: keywords
creator: Linus Bergqvist
creator: Adem Limani
creator: Bartosz Malman
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-12-01
publication date: 2025-12-01
starting page: 761
ending page: 778
doi: 10.54330/afm.177932

On \(L^p \to L^q\) infinitesimal relative boundedness of Schrödinger operators \((-\Delta)^{\alpha/2}+v\)
type: item
description: By analyzing the trace inequality for Bessel potentials, some Morrey-type sufficient conditions are given for which \(L^p \to L^q\), \(1<p,q<\infty\), infinitesimal relative boundedness of the Schrödinger operators \((-\Delta)^{\alpha/2}+v\) holds. These results provide new aspects of Morrey spaces and a nice application of weight theory.
subject: Articles
  topic: section
subject: Bessel potentials
  topic: keywords
subject: dyadic cubes
  topic: keywords
subject: infinitesimal relative bounds
  topic: keywords
subject: Morrey spaces
  topic: keywords
subject: Schrödinger operators
  topic: keywords
subject: trace inequality
  topic: keywords
subject: Wolff's potential
  topic: keywords
creator: Naoya Hatano
creator: Ryota Kawasumi
creator: Hiroki Saito
creator: Hitoshi Tanaka
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-11-17
publication date: 2025-11-17
starting page: 741
ending page: 759
doi: 10.54330/afm.177378

A step towards the tensorization of Sobolev spaces
type: item
description: We prove that Sobolev spaces on Cartesian and warped products of metric spaces tensorize, only requiring that one of the factors is a doubling space supporting a Poincaré inequality.
subject: Articles
  topic: section
subject: Sobolev space
  topic: keywords
subject: metric space
  topic: keywords
subject: doubling
  topic: keywords
subject: Cartesian product
  topic: keywords
subject: warped product
  topic: keywords
creator: Silvia Ghinassi
creator: Vikram Giri
creator: Elisa Negrini
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-11-12
publication date: 2025-11-12
starting page: 721
ending page: 740
doi: 10.54330/afm.177193

A variant of inverse mean curvature flow for star-shaped hypersurfaces evolving in a cone
type: item
description: Given a smooth convex cone in the Euclidean \((n+1)\)-space (\(n\geq 2\)), we consider strictly mean convex hypersurfaces with boundary which are star-shaped with respect to the center of the cone and which meet the cone perpendicularly. If those hypersurfaces inside the cone evolve by a variant of inverse mean curvature flow, then, by using the convexity of the cone in the derivation of the gradient and Hölder estimates, we can prove that this evolution exists for all the time and the evolving hypersurfaces converge smoothly to a piece of a round sphere as time tends to infinity.
subject: Articles
  topic: section
subject: Inverse mean curvature flow
  topic: keywords
subject: star-shaped
  topic: keywords
subject: Neumann boundary value problem
  topic: keywords
creator: Jing Mao
creator: Qiang Tu
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-11-07
publication date: 2025-11-07
starting page: 703
ending page: 720
doi: 10.54330/afm.177028

Anisotropic weighted Levin–Cochran–Lee type inequalities on homogeneous Lie groups
type: item
description: In this paper, we first prove the weighted Levin–Cochran–Lee type inequalities on homogeneous Lie groups for arbitrary weights, quasi-norms, and \(L^p\)- and \(L^q\)-norms. Then, we derive a sharp weighted inequality involving specific weights given in the form of quasi-balls in homogeneous Lie groups. Finally, we also calculate the sharp constants for the aforementioned inequalities.
subject: Articles
  topic: section
subject: Integral Hardy inequalities
  topic: keywords
subject: anisotropic Levin–Cochran–Lee inequalities
  topic: keywords
subject: homogeneous Lie groups
  topic: keywords
subject: quasi-norm
  topic: keywords
subject: weighted exponential inequalities
  topic: keywords
creator: Michael Ruzhansky
creator: Anjali Shriwastawa
creator: Bankteshwar Tiwari
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-11-06
publication date: 2025-11-06
starting page: 685
ending page: 701
doi: 10.54330/afm.176976

Directional pliability, Whitney extension, and Lusin approximation for curves in Carnot groups
type: item
description: We show that, in arbitrary Carnot groups, pliability in a subset of directions is sufficient to guarantee the existence of a Whitney-type extension and a Lusin approximation for curves with tangent vectors in the same set of directions. We apply this to show that every horizontal curve in the Engel group must intersect a \(C^{1}\) horizontal curve in a set of positive measure.
subject: Articles
  topic: section
subject: Whitney extension theorem
  topic: keywords
subject: Lusin approximation
  topic: keywords
subject: pliability
  topic: keywords
subject: Engel group
  topic: keywords
creator: Gareth Speight
creator: Scott Zimmerman
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-10-24
publication date: 2025-10-24
starting page: 665
ending page: 684
doi: 10.54330/afm.176524

Limits of manifolds with a Kato bound on the Ricci curvature. II
type: item
description: We prove that metric measure spaces obtained as limits of closed Riemannian manifolds with Ricci curvature satisfying a uniform Kato bound are rectifiable. In the case of a non-collapsing assumption and a strong Kato bound, we additionally show that for any \(\alpha \in (0,1)\) the regular part of the space lies in an open set with the structure of a \(C^\alpha\)-manifold.
subject: Articles
  topic: section
subject: Gromov–Hausdorff convergence
  topic: keywords
subject: Ricci curvature
  topic: keywords
subject: Kato class
  topic: keywords
subject: rectifiability
  topic: keywords
creator: Gilles Carron
creator: Ilaria Mondello
creator: David Tewodrose
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-10-22
publication date: 2025-10-22
starting page: 623
ending page: 663
doi: 10.54330/afm.176490

Generalized Schwarzians and normal families
type: item
description: We study families of analytic and meromorphic functions with bounded generalized Schwarzian derivative \(S_k(f)\). We show that these families are quasi-normal. Further, we investigate associated families, such as those formed by derivatives and logarithmic derivatives, and prove several (quasi-)normality results. Moreover, we derive a new formula for \(S_k(f)\), which yields a result for families \(F\subseteq H\mathbb{D}\) of locally univalent functions that satisfy \(S_k(f)(z)\neq b(z)\) for some \(b\in M(\mathbb{D})\) and all \(f\in F\), \(z\in\mathbb{C}\) and for entire functions \(g\) with \(S_k(g)(z)\neq 0\) and \(S_k(g)(z)\neq\infty\) for all \(z\in\mathbb{C}\). The classical Schwarzian derivative \(S_f\) is contained as the case \(k=2\).
subject: Articles
  topic: section
subject: Normal family
  topic: keywords
subject: Schwarzian derivative
  topic: keywords
subject: quasi-normality
  topic: keywords
subject: value distribution theory
  topic: keywords
creator: Matthias Grätsch
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-10-16
publication date: 2025-10-16
starting page: 611
ending page: 622
doi: 10.54330/afm.176369

Off-diagonal matrix extrapolation for Muckenhoupt bases
type: item
description: In this paper we extend the theory of Rubio de Francia extrapolation for matrix weights, recently introduced by Bownik and the first author (2022), to off-diagonal extrapolation. We also show that the theory of matrix weighted extrapolation can be extended to matrix \(A_p\) classes defined with respect to a general basis, provided that a version of the Christ–Goldberg maximal operator is assumed to be bounded. Finally, we extend a recent result by Vuorinen (2024) and show that all of the multiparameter bases have this property.
subject: Articles
  topic: section
subject: Convex-set valued functions
  topic: keywords
subject: maximal operators
  topic: keywords
subject: off-diagonal inequalities
  topic: keywords
subject: Muckenhoupt weights
  topic: keywords
subject: matrix weights
  topic: keywords
subject: Rubio de Francia extrapolation
  topic: keywords
creator: David Cruz-Uribe OFS
creator: Fatih Şirin
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-10-14
publication date: 2025-10-14
starting page: 577
ending page: 609
doi: 10.54330/afm.176290

Carathéodory convergence and the conformal type problem
type: item
description: We study Carathédory convergence for open, simply connected surfaces spread over the sphere and, in particular, provide examples demonstrating that in the Speiser class the conformal type can change when two singular values collide.
subject: Articles
  topic: section
subject: Riemann surface
  topic: keywords
subject: type problem
  topic: keywords
subject: Speiser class
  topic: keywords
creator: Alexandre Eremenko
creator: Sergei Merenkov
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-10-06
publication date: 2025-10-06
starting page: 563
ending page: 575
doi: 10.54330/afm.176092

Greedy matching in optimal transport with concave cost
type: item
description: We consider the optimal transport problem between a set of \(n\) red points and a set of \(n\) blue points subject to a concave cost function such as \(c(x,y) = \|x-y\|^p\) for \(0< p < 1\). Our focus is on a particularly simple matching algorithm: match the closest red and blue point, remove them both and repeat. We prove that it provides good results in any metric space \((X,d)\) when the cost function is \(c(x,y) = d(x,y)^{p}\) with \(0 < p < 1/2\). Empirically, the algorithm produces results that are remarkably close to optimal—especially as the cost function gets more concave; this suggests that greedy matching may be a good toy model for optimal transport for very concave transport cost.
subject: Articles
  topic: section
subject: Optimal transport
  topic: keywords
subject: Euclidean random assignment problems
  topic: keywords
creator: Andrea Ottolini
creator: Stefan Steinerberger
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-09-18
publication date: 2025-09-18
starting page: 549
ending page: 562
doi: 10.54330/afm.173113

Matrix-weighted bounds in variable Lebesgue spaces
type: item
description: In this paper we prove boundedness of Calderón–Zygmund operators and the Christ–Goldberg maximal operator in the matrix-weighted variable Lebesgue spaces recently introduced by Cruz-Uribe and the second author. Our main tool to prove these bounds is through bounding a Goldberg auxiliary maximal operator. As an application, we obtain a quantitative extrapolation theorem for matrix-weighted variable Lebesgue spaces from the recent framework of directional Banach function spaces of the first author.
subject: Articles
  topic: section
subject: Singular integrals
  topic: keywords
subject: Calderón–Zygmund operators
  topic: keywords
subject: variable Lebesgue spaces
  topic: keywords
subject: exponent functions
  topic: keywords
subject: maximal operators
  topic: keywords
subject: matrix weights
  topic: keywords
subject: convex body domination
  topic: keywords
creator: Zoe Nieraeth
creator: Michael Penrod
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-09-01
publication date: 2025-09-01
starting page: 519
ending page: 548
doi: 10.54330/afm.164106

A dual simple proof of the classical Bernstein and Calabi–Bernstein theorems
type: item
description: In this note, we present a short and simple proof of both the Bernstein theorem and the Calabi–Bernstein theorem, which allows us to visualize both the common features and the remarkable differences between the two results. The proofs are based on the construction of conformal metrics that ensure the parabolicity of the surfaces. Consequently, they do not rely on complex analysis.
subject: Articles
  topic: section
subject: Nonlinear PDE of divergence form
  topic: keywords
subject: uniqueness of entire solutions
  topic: keywords
creator: Daniel de la Fuente
creator: Rafael M. Rubio
creator: Jose Torrente-Teruel
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-26
publication date: 2025-08-26
starting page: 511
ending page: 518
doi: 10.54330/afm.163974

Sharp Fourier decay estimates for measures supported on the well-approximable numbers
type: item
description: We construct a measure on the well-approximable numbers whose Fourier transform decays at a nearly optimal rate. This gives a logarithmic improvement on a previous construction of Kaufman.
subject: Articles
  topic: section
subject: Harmonic analysis
  topic: keywords
subject: geometric measure theory
  topic: keywords
subject: Diophantine approximation
  topic: keywords
subject: Hausdorff dimension
  topic: keywords
creator: Robert Fraser
creator: Thanh Nguyen
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-25
publication date: 2025-08-25
starting page: 483
ending page: 510
doi: 10.54330/afm.163951

Exceptional set estimates in finite fields
type: item
description: We study the exceptional set estimate for projections in \(\mathbb{F}_q^n\). For each \(V\in G(k,\mathbb{F}^n_q)\), let \(\pi_V\colon \mathbb{F}_q^n\rightarrow V\) be the projection map. We prove the following result: If \(A\subset \mathbb{F}_q^n\) with \(\#A=q^a\) (\(n-1\le a\le n\)) and \(0< s<\frac{a+n-2}{2}\), then \(\# \{V\in G(n-1,\mathbb{F}^n_q)\colon \#\pi_V(A)< q^s \}\lessapprox q^{n-2}\). This improves the previous range \(0<s<\frac{n-1}{n}a\). Also, our range of \(s\) is sharp in the sense that if \(s>\frac{a+n-2}{2}\), then the right hand side above should be at least \(q^t\) for some \(t>n-2\).
subject: Articles
  topic: section
subject: Projection theory
  topic: keywords
subject: exceptional set estimate
  topic: keywords
creator: Paige Bright
creator: Shengwen Gan
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-12
publication date: 2025-08-12
starting page: 467
ending page: 481
doi: 10.54330/afm.163667

Two footnotes to the F. & M. Riesz theorem
type: item
description: We present a new proof of the F. & M. Riesz theorem on analytic measures of the unit circle \(\mathbb{T}\) that is based the following elementary inequality: If \(f\) is analytic in the unit disc \(\mathbb{D}\) and \(0 \leq r \leq \varrho < 1\), then \(\|f_r-f_\varrho\|_1 \leq 2 \sqrt{\|f_\varrho\|_1^2-\|f_r\|_1^2}\), where \(f_r(e^{i\theta})=f(r e^{i\theta})\) and where \(\|\cdot\|_1\) denotes the norm of \(L^1(\mathbb{T})\). The proof extends to the infinite-dimensional torus \(\mathbb{T}^\infty\), where it clarifies the relationship between Hilbert's criterion for \(H^1(\mathbb{T}^\infty)\) and the F. & M. Riesz theorem.
subject: Articles
  topic: section
subject: Analytic measures
  topic: keywords
subject: Hardy spaces
  topic: keywords
subject: infinite-dimensional torus
  topic: keywords
creator: Ole Fredrik Brevig
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-06
publication date: 2025-08-06
starting page: 459
ending page: 466
doi: 10.54330/afm.163565

On bounded energy of convolution of fractal measures
type: item
description: For all \(s\in[0,1]\) and \(t\in(0,s]\cup [2-s,2)\), we find the supremum of numbers \(\omega\in(0,2)\) such that \(\textup{I}_\omega(\mu\ast\sigma) \lesssim 1,\) where \(\mu\) is any Borel measure on \(B(1)\) with \(\textup{I}_t(\mu)\leq 1\) and \(\sigma\) is any \((s,1)\)-Frostman measure on a \(C^2\)-graph with non-zero curvature. As an application, we use this to show the sharp \(L^6\)-decay of Fourier transform of \(\sigma\) when \(s\in [\frac{2}{3}, 1]\).
subject: Articles
  topic: section
subject: Incidences
  topic: keywords
subject: Riesz energy
  topic: keywords
subject: Fourier decay
  topic: keywords
creator: Guangzeng Yi
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-04
publication date: 2025-08-04
starting page: 437
ending page: 457
doi: 10.54330/afm.163545

Covering sponges with tubes
type: item
description: The aim of this note is to give a short proof of a result of Pyörälä–Shmerkin–Suomala–Wu; the Sierpiński carpet, and generalisations, are tube-null; they can be covered with tubes of arbitrarily small total width. We remark that a more general class of sponge-like sets satisfy this property. For a given \(\epsilon > 0\) the proof is able to give an explicit description of the tubes for which the total width is less than \(\epsilon\).
subject: Articles
  topic: section
subject: Tube-null
  topic: keywords
subject: orthogonal projection
  topic: keywords
creator: William O'Regan
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-08-03
publication date: 2025-08-03
starting page: 423
ending page: 435
doi: 10.54330/afm.163515

Conformal and holomorphic barycenters in hyperbolic balls
type: item
description: We introduce the notions of conformal barycenter and holomorphic barycenter of a measurable set \(D\) in the hyperbolic ball. The two barycenters coincide in the disk, but they differ in multidimensional balls of \(\mathbb{C}^m \cong \mathbb{R}^{2m}\). These notions are counterparts of barycenters of measures on spheres, introduced by Douady and Earle in 1986.
subject: Articles
  topic: section
subject: Möbius tranformations
  topic: keywords
subject: automorphisms
  topic: keywords
subject: unit ball
  topic: keywords
subject: convex potentials
  topic: keywords
creator: Vladimir Jaćimović
creator: David Kalaj
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-07-16
publication date: 2025-07-16
starting page: 407
ending page: 421
doi: 10.54330/afm.163349

A counting formula for extreme contractions on regular polygonal Banach spaces
type: item
description: A regular polygonal Banach space \(X\) is a two-dimensional real Banach space whose unit sphere is a regular polygon. We prove that the number of extreme contractions on a regular \(2n\)-gonal Banach space is \(2n^2+4n\). A characterization of extreme contractions on \(X\) is also presented.
subject: Articles
  topic: section
subject: Polygonal Banach space
  topic: keywords
subject: extreme contraction
  topic: keywords
subject: support functional
  topic: keywords
subject: isometry
  topic: keywords
creator: Lakshmi Kanta Dey
creator: Subhadip Pal
creator: Saikat Roy
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-07-01
publication date: 2025-07-01
starting page: 389
ending page: 405
doi: 10.54330/afm.163218

A deterministic proof of Loewner energy reversibility via local reversals
type: item
description: We give a new proof of the orientation reversibility of chordal Loewner energy by reversing the orientation of a chord in partial increments. This fact was first proved by Wang (2019) using the reversibility of chordal Schramm–Loewner evolution (SLE) along with the interpretation of Loewner energy as the large deviation rate function of chordal SLE\(_\kappa\) as \(\kappa \to 0\). Our method is similar in spirit to Zhan's proof (2008) of chordal SLE\(_\kappa\) reversibility for \(\kappa \in (0,4]\), though it is purely deterministic. As a key step in our proof, we establish that a minimal energy chord among those passing through a fixed finite set of points is a piecewise hyperbolic geodesic.
subject: Articles
  topic: section
subject: Loewner energy
  topic: keywords
subject: orientation reversibility
  topic: keywords
subject: commutation relation
  topic: keywords
subject: piecewise geodesic
  topic: keywords
creator: Jinwoo Sung
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-06-29
publication date: 2025-06-29
starting page: 371
ending page: 387
doi: 10.54330/afm.163173

Finite dimensionality of Besov spaces and potential-theoretic decomposition of metric spaces
type: item
description: In the context of a metric measure space \((X,d,\mu)\), we explore the potential-theoretic implications of having a finite-dimensional Besov space. We prove that if the dimension of the Besov space \(B^\theta_{p,p}(X)\) is \(k>1\), then \(X\) can be decomposed into \(k\) number of irreducible components (Theorem 1.1). Note that \(\theta\) may be bigger than \(1\), as our framework includes fractals. We also provide sufficient conditions under which the dimension of the Besov space is 1. We introduce critical exponents \(\theta_p(X)\) and \(\theta_p^{\ast}(X)\) for the Besov spaces. As examples illustrating Theorem 1.1, we compute these critical exponents for spaces \(X\) formed by glueing copies of \(n\)-dimensional cubes, the Sierpiński gaskets, and of the Sierpiński carpet.
subject: Articles
  topic: section
subject: Besov spaces
  topic: keywords
subject: Korevaar–Schoen spaces
  topic: keywords
subject: fractal
  topic: keywords
subject: irreducible p-energy form
  topic: keywords
subject: Newton–Sobolev spaces
  topic: keywords
subject: p-Poincaré inequality
  topic: keywords
subject: Sierpiński fractals
  topic: keywords
subject: decomposition
  topic: keywords
creator: Takashi Kumagai
creator: Nageswari Shanmugalingam
creator: Ryosuke Shimizu
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-06-27
publication date: 2025-06-27
starting page: 347
ending page: 369
doi: 10.54330/afm.163110

The Stepanov theorem for Q-valued functions
type: item
description: In this work we prove the Stepanov differentiation theorem for multiple-valued functions. This theorem is proved in the wide generality of metric-space-multiple-valued functions without relying on a Lipschitz extension result. General definitions of differentiability and approximate differentiability for functions between suitable metric spaces are also introduced.
subject: Articles
  topic: section
subject: Lipschitz functions
  topic: keywords
subject: Rademacher's theorem
  topic: keywords
subject: multiple-valued functions
  topic: keywords
subject: Stepanov's theorem
  topic: keywords
subject: metric measure spaces
  topic: keywords
creator: Paolo De Donato
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-06-21
publication date: 2025-06-21
starting page: 331
ending page: 345
doi: 10.54330/afm.162970

Normalized solutions for logarithmic Schrödinger equation with a perturbation of power law nonlinearity
type: item
description: We study the existence of normalized solutions to the following logarithmic Schrödinger equation \(-\Delta u+\lambda u=\alpha u\log u^2+\mu|u|^{p-2}u\), \(x\in\mathbb{R}^N\), under the mass constraint \(\int_{\mathbb{R}^N}u^2\,\mathrm{d}x=c^2\), where \(\alpha,\mu\in\mathbb{R}\), \(N\ge 2\), \(p>2\), \(c>0\) is a constant, and \(\lambda\in\mathbb{R}\) appears as Lagrange multiplier. Under different assumptions on \(\alpha\), \(\mu\), \(p\) and \(c\), we prove the existence of ground state solutions and excited state solutions. The asymptotic behavior of the ground state solution as \(\mu\to 0\) is also investigated. Our results include the case \(\alpha<0\) or \(\mu<0\), which is less studied in the literature.
subject: Articles
  topic: section
subject: Logarithmic Schrödinger equation
  topic: keywords
subject: normalized solution
  topic: keywords
subject: variational methods
  topic: keywords
creator: Wei Shuai
creator: Xiaolong Yang
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-05-20
publication date: 2025-05-20
starting page: 301
ending page: 330
doi: 10.54330/afm.161873

Unique extremality of affine maps on plane domains
type: item
description: We prove that affine maps are uniquely extremal quasiconformal maps on the complement of a well distributed set in the complex plane answering a conjecture from Marković (2002). We construct the required Reich sequence using Bergman projections, and meromorphic partitions of unity.
subject: Articles
  topic: section
subject: Extremal quasiconformal maps
  topic: keywords
subject: Bergman projection on plane domains
  topic: keywords
creator: Qiliang Luo
creator: Vladimir Marković
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-05-14
publication date: 2025-05-14
starting page: 287
ending page: 299
doi: 10.54330/afm.161692

On the sharp second order Caffarelli–Kohn–Nirenberg inequality
type: item
description: The purpose of this paper is twofold. By developing a new technique, we first prove some sharp Caffarelli–Kohn–Nirenberg inequalities of second order for non-radial functions. As a direct consequence, we recover the sharp second order uncertainty principle in Cazacu, Flynn and Lam (2022). For the class of radial functions, we next establish a sharp inequality which can be regarded as the second order version of Xia's inequality (2007).
subject: Articles
  topic: section
subject: Caffarelli–Kohn–Nirenberg inequalities
  topic: keywords
subject: uncertainty principle
  topic: keywords
subject: sharp constants
  topic: keywords
subject: extremal functions
  topic: keywords
creator: Anh Tuan Duong
creator: Van Hoang Nguyen
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-05-06
publication date: 2025-05-06
starting page: 275
ending page: 286
doi: 10.54330/afm.161506

Logarithmic vanishing theorems on weakly 1-complete Kähler manifolds
type: item
description: This paper aims to investigate the vanishing theorems of cohomology groups on weakly 1-complete Kähler manifolds. Firstly, we extend a logarithmic vanishing theorem originally proposed by Huang, Liu, Wan and Yang, which says that when \(N\otimes \mathcal{O}_X([\Delta])\) is a \(k\)-positive \(\mathbb{R}\)-line bundle, the \(q\)-th cohomology group of sheaf \(\Omega^{p}(\log D)\otimes L\otimes N\) vanishes for any \(p+q\geq n+k+1\) over a compact Kähler manifold \(X\). The proof employs an approximation theorem. In the local case, the result follows directly as a corollary of the original theorem. In the global case, we construct a solution for any positive real number \(c\), ensuring that the error term with respect to the exact solution converges to zero in the sense of norm. Finally, as applications of our results, we obtain logarithmic generalizations of several classical vanishing theorems and the corresponding corollaries.
subject: Articles
  topic: section
subject: Logarithmic vanishing theorem
  topic: keywords
subject: simple normal crossing divisor
  topic: keywords
subject: weakly 1-complete manifolds
  topic: keywords
subject: approximation theorem
  topic: keywords
creator: Shilong Lu
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-05-02
publication date: 2025-05-02
starting page: 253
ending page: 274
doi: 10.54330/afm.161414

A clustering theorem in fractional Sobolev spaces
type: item
description: We prove a general clustering result for the fractional Sobolev space \(W^{s,p}\): whenever the positivity set of a function \(u\) in a cube has measure bounded from below by a multiple of the cube's volume, and the \(W^{s,p}\)-seminorm of \(u\) is bounded from above by a convenient power of the cube's side, then \(u\) is positive in a universally reduced cube. Our result aims at applications in regularity theory for fractional elliptic and parabolic equations. Also, by means of suitable interpolation inequalities, we show that clustering results in \(W^{1,p}\) and \(BV\), respectively, can be deduced as special cases.
subject: Articles
  topic: section
subject: Clustering
  topic: keywords
subject: fractional Sobolev spaces
  topic: keywords
subject: regularity
  topic: keywords
creator: Fatma Gamze Düzgün
creator: Antonio Iannizzotto
creator: Vincenzo Vespri
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-04-29
publication date: 2025-04-29
starting page: 243
ending page: 252
doi: 10.54330/afm.161328

CMC hypersurfaces with polynomial volume growth in warped products and the nonexistence of entire solutions to the minimal hypersurface equation
type: item
description: We investigate constant mean curvature (CMC) complete two-sided hypersurfaces with polynomial volume growth in a class of warped products satisfying a suitable curvature constraint. In this setting, we establish the nonexistence of such a CMC hypersurface under mild hypotheses involving the mean curvature and the warping function. Applications to Einstein warped product, pseudo-hyperbolic, Schwarzschild and Reissner–Nordström spaces are also given. Furthermore, we present a nonparametric version of our main result which, in particular, guarantees the nonexistence of entire solutions with finite C2 norm of the the minimal hypersurface equation on a complete Riemannian manifold with polynomial volume growth.
subject: Articles
  topic: section
subject: Warped products
  topic: keywords
subject: constant mean curvature two-side hypersurfaces
  topic: keywords
subject: polynomial volume growth
  topic: keywords
subject: minimal hypersurfaces
  topic: keywords
subject: entire graphs
  topic: keywords
creator: Henrique Fernandes de Lima
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-04-28
publication date: 2025-04-28
starting page: 231
ending page: 241
doi: 10.54330/afm.161311

The Landau–Bloch type theorems for certain class of holomorphic and pluriharmonic mappings in C^n
type: item
description: In this paper, we define two classes of holomorphic mappings defined on the unit ball \(B^n\) of \(n\)-dimensional complex space \(\mathbb{C}^n\) and obtain the lower estimates for Bloch's constant for these classes. Also, we derive the Landau–Bloch type theorem for some subclasses of pluriharmonic mappings defined on the unit ball \(B^n\).
subject: Articles
  topic: section
subject: Holomorphic mapping
  topic: keywords
subject: quasiregular mapping
  topic: keywords
subject: (K,K')-elliptic mapping
  topic: keywords
subject: quasiconformal mapping
  topic: keywords
subject: Landau–Bloch type theorem
  topic: keywords
subject: pluriharmonic mapping
  topic: keywords
creator: Vasudevarao Allu
creator: Rohit Kumar
rights: Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0
date: 2025-04-10
publication date: 2025-04-10
starting page: 215
ending page: 229
doi: 10.54330/afm.160790