On the embedding between the variable Lebesgue space L <SUP>p (<middle dot>) </SUP>(Ω) and the Orlicz space L (log L )<SUP>α</SUP> (Ω)

作     者：Cruz-Uribe, David Gogatishvili, Amiran Kopaliani, Tengiz 

作者机构：Univ Alabama Dept Math Tuscaloosa AL 35487 USA Czech Acad Sci Inst Math Zitna 25 Prague 1 Czech Republic I Javakhishvili Tbilisi State Univ Fac Exact & Nat Sci Univ St 2 Tbilisi 0143 Georgia 

出 版 物：《JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS》 (J. Math. Anal. Appl.)

年 卷 期：2025年第544卷第2期

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Simons Foundation Travel Support for Mathematicians Grant NSF [DMS-2349550] Czech Academy of Sciences [RVO: 67985840] Czech Science Foundation (GACR) [23-04720S] Shota Rustaveli National Science Foundation (SRNSF) [FR 21-12353] 

主　　题：Banach function spaces Variable Lebesgue spaces Zygmund spaces 

摘      要：We give a sharp sufficient condition on the distribution function, |{x is an element of Q : p ( x ) 0, of the exponent function p () : Q - [1, infinity) that implies the embedding of the variable Lebesgue space L p ( ) (Q) into the Orlicz space L (log L ) alpha (Q), alpha 0, where Q is an open set with finite Lebesgue measure. As applications of our results, we first give conditions that imply the strong differentiation of integrals of functions in L p ( ) ((0 , 1)n), n 1. We then consider the integrability of the maximal function on variable Lebesgue spaces, where the exponent function p () approaches 1 in value on some part of the domain. This result is an improvement of the result in [6]. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.