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/).
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页数：17
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