Hardy-Littlewood maximal operator on reflexive variable Lebesgue spaces over spaces of homogeneous type

被引：0

作者：

Karlovich, Alexei ^{[1
]}

机构：

[1] Univ Nova Lisboa, Fac Ciencias & Tecnol, Dept Matemat, Ctr Matemat & Aplicacoes, P-2829516 Quinta Da Torre, Caparica, Portugal

来源：

STUDIA MATHEMATICA | 2020年 / 254卷 / 02期

关键词：

Hardy-Littlewood maximal operator; variable Lebesgue space; space of homogeneous type; dyadic cubes; PROPERTY;

D O I：

10.4064/sm180816-16-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the Hardy-Littlewood maximal operator is bounded on a reflexive variable Lebesgue space L-p(.) over a space of homogeneous type (X, d, mu) if and only if it is bounded on its dual space L-p'(.), where 1/p(x) + 1/p' (x) = 1 for x is an element of X. This result extends the corresponding result of Lars Diening from the Euclidean setting of R-n to the setting of spaces (X, d, mu) of homogeneous type.

引用

页码：149 / 178

页数：30

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