On the modulus of continuity of fractional Orlicz-Sobolev functions

IF 1.3 2区 数学 Q1 MATHEMATICS Mathematische Annalen Pub Date : 2024-09-02 DOI:10.1007/s00208-024-02964-z
Angela Alberico, Andrea Cianchi, Luboš Pick, Lenka Slavíková
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Abstract

Necessary and sufficient conditions are presented for a fractional Orlicz-Sobolev space on \({\mathbb {R}}^n\) to be continuously embedded into a space of uniformly continuous functions. The optimal modulus of continuity is exhibited whenever these conditions are fulfilled. These results pertain to the supercritical Sobolev regime and complement earlier sharp embeddings into rearrangement-invariant spaces concerning the subcritical setting. Classical embeddings for fractional Sobolev spaces into Hölder spaces are recovered as special instances. Proofs require novel strategies, since customary methods fail to produce optimal conclusions.

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论分数奥立兹-索博列夫函数的连续性模数
提出了将\({\mathbb {R}}^n\) 上的分数奥利兹-索博廖夫空间连续嵌入到均匀连续函数空间的必要条件和充分条件。只要满足这些条件,就会显示出最优的连续性模量。这些结果与超临界索博廖夫机制有关,是对早先关于次临界设置的锐嵌入到重排不变空间的补充。分数 Sobolev 空间到霍尔德空间的经典嵌入作为特例得到了恢复。由于传统方法无法得出最佳结论,因此证明需要新颖的策略。
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来源期刊
Mathematische Annalen
Mathematische Annalen 数学-数学
CiteScore
2.90
自引率
7.10%
发文量
181
审稿时长
4-8 weeks
期刊介绍: Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin. The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin. Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.
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