EXTRAPOLATION AND INTERPOLATION IN GENERALIZED ORLICZ SPACES

被引：55

作者：

Cruz-Uribe, David ^{[1
]}

Hasto, Peter ^{[2
,3
]}

机构：

[1] Univ Alabama, Dept Math, Tuscaloosa, AL 35487 USA

[2] Univ Oulu, Dept Math Sci, POB 3000, FI-90014 Oulu, Finland

[3] Univ Turku, Dept Math & Stat, FI-20014 Turku, Finland

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 370卷 / 06期

基金：

美国国家科学基金会;

关键词：

Non-standard growth; variable exponent; Musielak-Orlicz spaces; extrapolation; weighted norm inequalities; WEIGHTED NORM INEQUALITIES; YOUNG TYPE INEQUALITIES; VARIABLE EXPONENT; MAXIMAL FUNCTIONS; APPROXIMATE IDENTITIES; FUNCTIONALS; LEBESGUE; OPERATORS; FACTORIZATION; COMMUTATORS;

D O I：

10.1090/tran/7155

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove versions of the Rubio de Francia extrapolation theorem in generalized Orlicz spaces. As a consequence, we obtain boundedness results for several classical operators as well as a Sobolev inequality in this setting. We also study complex interpolation in the same setting and use it to derive a compact embedding theorem. Our results include as special cases classical Lebesgue and Sobolev space estimates and their variable exponent and double phase growth analogs.

引用

页码：4323 / 4349

页数：27

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[1] On some new non-linear diffusion models for the image filtering [J].