Annales Fennici Mathematici https://afm.journal.fi/ <p>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.</p> en-US pekka.j.koskela@jyu.fi (Pekka Koskela) mika.koskenoja@helsinki.fi (Mika Koskenoja) Thu, 02 Jan 2025 14:08:26 +0200 OJS 3.2.1.4 http://blogs.law.harvard.edu/tech/rss 60 Quantitative Sobolev regularity of quasiregular maps https://afm.journal.fi/article/view/155498 <pre>We quantify the Sobolev space norm of the Beltrami resolvent \((I- \mu S)^{-1}\), where \(S\) is the Beurling–Ahlfors transform, in terms of the corresponding Sobolev space norm of the dilatation \(\mu\) in the critical and supercritical ranges. Our estimate entails as a consequence quantitative self-improvement inequalities of Caccioppoli type for quasiregular distributions with dilatations in \(W^{1,p}\), \(p \ge 2\). Our proof strategy is then adapted to yield quantitative estimates for the resolvent \((I-\mu S_\Omega)^{-1}\) of the Beltrami equation on a sufficiently regular domain \(\Omega\), with \(\mu\in W^{1,p}(\Omega)\). Here, \(S_\Omega\) is the compression of \(S\) to a domain \(\Omega\). Our proofs do not rely on the compactness or commutator arguments previously employed in related literature. Instead, they leverage the weighted Sobolev estimates for compressions of Calderón–Zygmund operators to domains, recently obtained by the authors, to extend the Astala–Iwaniec–Saksman technique to higher regularities.</pre> Francesco Di Plinio, A. Walton Green, Brett D. Wick Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0 https://afm.journal.fi/article/view/155498 Thu, 02 Jan 2025 00:00:00 +0200 Tent spaces and solutions of Weinstein type equations with CMO(R_+,dm_λ) boundary values https://afm.journal.fi/article/view/155908 <p> </p> <pre>Let \(\{P_{t}^{[\lambda]}\}_{t&gt;0}\) be the Poisson semigroup associated with the Bessel operator \(\Delta_{\lambda}\) on \(\mathbb{R}_+:=(0,\infty)\), where \(\lambda&gt;0\) and</pre> <pre> </pre> <pre>\(\Delta_{\lambda}:=-x^{-2\lambda}\frac{d}{dx}x^{2\lambda}\frac{d}{dx}\).</pre> <pre> </pre> <pre>In this paper, the authors show that a function \(u(y,t)\) on \(\mathbb{R}_{+}\times\mathbb{R}_{+}\), has the form \(u(y,t)=P_{t}^{[\lambda]}f(y)\) with \(f\in\) CMO\((\mathbb{R}_{+},dm_{\lambda})\), where \(dm_{\lambda}(x):=x^{2\lambda}\,dx\), if and only if \(u\) satisfies the Weinstein type equation</pre> <pre> </pre> <pre>\(\mathbb{L}_{\lambda}u(x,t):=\frac{\partial^{2}u(x,t)}{\partial t^{2}}-\Delta_{\lambda}u(x,t)=0\), \((x,t)\in{\mathbb{R}_{+}\times\mathbb{R}_{+}}\),</pre> <pre> </pre> <pre>a Carleson type condition and certain limiting conditions. For this purpose, the authors first introduce the tent spaces \(T_{2}^{p}\) with \(p\in[1,\infty]\) and \(T_{2,C}^{\infty}\) in the Bessel setting and then show that CMO\((\mathbb{R}_{+},dm_{\lambda})\) has a connection with \(T_{2,C}^{\infty}\) via \(\{P_{t}^{[\lambda]}\}_{t&gt;0}\). In addition, the authors obtain some boundedness results on the operator \(\pi_{\lambda}\) from tent spaces to some "ordinary" function spaces.</pre> <p> </p> Jorge J. Betancor, Qingdong Guo, Dongyong Yang Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0 https://afm.journal.fi/article/view/155908 Thu, 09 Jan 2025 00:00:00 +0200 A note on summability in Banach spaces https://afm.journal.fi/article/view/156613 <pre>Let \(Z\) and \(X\) be Banach spaces. Suppose that \(X\) is Asplund. Let \(\mathcal{M}\) be a bounded set of operators from \(Z\) to \(X\) with the following property: a bounded sequence \((z_n)_{n\in \mathbb{N}}\) in \(Z\) is weakly null if, for each \(M\in\mathcal{M}\), the sequence \((M(z_n))_{n\in\mathbb{N}}\) is weakly null. Let \((z_n)_{n\in\mathbb{N}}\) be a sequence in \(Z\) such that: (a) for each \(n\in\mathbb{N}\), the set \(\{M(z_n)\colon M\in \mathcal{M}\}\) is relatively norm compact; (b) for each sequence \((M_n)_{n\in\mathbb{N}}\) in \(\mathcal{M}\), the series \(\sum_{n=1}^\infty M_n(z_n)\) is weakly unconditionally Cauchy. We prove that if \(T\in \mathcal{M}\) is Dunford–Pettis and \(\inf_{n\in\mathbb{N}}\|T(z_n)\|\|z_n\|^{-1}&gt;0\), then the series \(\sum_{n=1}^\infty T(z_n)\) is absolutely convergent. As an application, we provide another proof of the fact that a countably additive vector measure taking values in an Asplund Banach space has finite variation whenever its integration operator is Dunford–Pettis.</pre> José Rodríguez Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0 https://afm.journal.fi/article/view/156613 Thu, 30 Jan 2025 00:00:00 +0200 The dimension of projections of planar diagonal self-affine measures https://afm.journal.fi/article/view/156815 <pre>We show that if \(\mu\) is a self-affine measure on the plane defined by an iterated function system of contractions with diagonal linear parts, then under an irrationality assumption on the entries of the linear parts,</pre> <pre> <br />\(\operatorname{dim}_{\rm H} \mu \circ \pi^{-1} = \min \{ 1, \operatorname{dim}_{\rm H} \mu \}\)<br /> </pre> <pre>for any non-principal orthogonal projection \(\pi\).</pre> Aleksi Pyörälä Copyright (c) 2025 Annales Fennici Mathematici https://creativecommons.org/licenses/by-nc/4.0 https://afm.journal.fi/article/view/156815 Fri, 07 Feb 2025 00:00:00 +0200