On \(L^p \to L^q\) infinitesimal relative boundedness of Schrödinger operators \((-\Delta)^{\alpha/2}+v\)

Authors

  • Naoya Hatano Chuo University, Department of Mathematics
  • Ryota Kawasumi Gunma University, Center for Mathematics and Data Science
  • Hiroki Saito Nihon University, College of Science and Technology
  • Hitoshi Tanaka National University Corporation Tsukuba University of Technology, Research and Support Center on Higher Education for the Hearing and Visually Impaired

DOI:

https://doi.org/10.54330/afm.177378

Keywords:

Bessel potentials, dyadic cubes, infinitesimal relative bounds, Morrey spaces, Schrödinger operators, trace inequality, Wolff's potential

Abstract

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.

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Published

2025-11-17

Issue

Vol. 50 No. 2 (2025)

Section

Articles

License

Copyright (c) 2025 Annales Fennici Mathematici

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

Hatano, N., Kawasumi, R., Saito, H., & Tanaka, H. (2025). On \(L^p \to L^q\) infinitesimal relative boundedness of Schrödinger operators \((-\Delta)^{\alpha/2}+v\). Annales Fennici Mathematici, 50(2), 741–759. https://doi.org/10.54330/afm.177378