BANACH FUNCTION SPACES ON LOCALLY COMPACT GROUPS

被引：5

作者：

Gorka, Przemyslaw ^{[1
]}

Pospiech, Pawel ^{[1
]}

机构：

[1] Warsaw Univ Technol, Dept Math & Informat Sci, Ul Koszykowa 75, PL-00662 Warsaw, Poland

来源：

ANNALS OF FUNCTIONAL ANALYSIS | 2019年 / 10卷 / 04期

关键词：

Banach function spaces; topological groups; compactness; Riesz-Kolmogorov theorem; Sudakov theorem;

D O I：

10.1215/20088752-2019-0002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study Banach function spaces (BFS) on locally compact topological groups. We focus on totally bounded sets in BFS. We obtain the Riesz-Kolmogorov compactness theorem as well as the Sudakov theorem.

引用

页码：460 / 471

页数：12

共 27 条

[1]

[Anonymous], 1932, Bull. Amer. Math. Soc, DOI [10.1090/S0002-9904-1932-05332-0, DOI 10.1090/S0002-9904-1932-05332-0]

[2]

[Anonymous], 2009, Proc. A. Razmadze Math. Inst.

[3]

[Anonymous], 1957, Usp. Mat. Nauk

[4]

[Anonymous], 1937, Acta Litt. Sci. Szeged

[5] RELATIVELY COMPACT SETS IN VARIABLE-EXPONENT LEBESGUE SPACES [J].

Bandaliyev, Rovshan ;

Gorka, Przemyslaw .

BANACH JOURNAL OF MATHEMATICAL ANALYSIS, 2018, 12 (02) :331-346

[6]

Bennett C., 1988, INTERPOLATION OPERAT, V129

[7] Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces [J].

Caetano, Antonio ;

Gogatishvili, Amiran ;

Opic, Bohumir .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2016, 146 (05) :905-927

[8]

Deitmar A, 2009, UNIVERSITEXT, P1, DOI 10.1007/978-0-387-85469-4_1

[9] Lebesgue and Sobolev Spaces with Variable Exponents [J].

Diening, Lars ;

Harjulehto, Petteri ;

Hasto, Peter ;

Ruzicka, Michael .

LEBESGUE AND SOBOLEV SPACES WITH VARIABLE EXPONENTS, 2011, 2017 :1-+

[10] LIGHT SIDE OF COMPACTNESS IN LEBESGUE SPACES: SUDAKOV THEOREM [J].

Gorka, Przemyslaw ;

Rafeiro, Humberto .

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2017, 42 (01) :135-139

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