On grand Sobolev spaces and pointwise description of Banach function spaces

被引：8

作者：

Jain, Pankaj ^{[1
]}

Molchanova, Anastasia ^{[2
,3
]}

Singh, Monika ^{[4
]}

Vodopyanov, Sergey ^{[2
]}

机构：

[1] South Asian Univ, Dept Math, New Delhi 110021, India

[2] Sobolev Inst Math, Acad Koptyug Ave 4, Novosibirsk 630090, Russia

[3] TU Wien, Inst Anal & Sci Comp, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria

[4] Univ Delhi, Dept Math, Lady Shri Ram Coll Women, New Delhi 110024, India

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2021年 / 202卷

基金：

奥地利科学基金会;

关键词：

Banach function space; Grand Sobolev space; Maximal function; Pointwise description; WEIGHTED NORM INEQUALITIES; LEBESGUE SPACES; PARABOLIC EQUATIONS; MAXIMAL FUNCTIONS; INTEGRABILITY; REGULARITY; EXISTENCE;

D O I：

10.1016/j.na.2020.112100

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain a pointwise description of functions belonging to function spaces with the lattice property. In particular, it is valid for Banach function spaces provided that the Hardy-Littlewood maximal operator is bounded. We also study weighted grand Sobolev spaces, defined on arbitrary open sets Omega (of finite or infinite measure) in R-n, and provide pointwise description of them. (c) 2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

引用

页数：17

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