On the compactness in grand spaces

Humberto Rafeiro; Andrés Vargas

doi:10.1515/gmj-2014-0060

On the compactness in grand spaces

Humberto Rafeiro, Andrés Vargas

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

In this paper we study compactness of subsets of grand Lebesgue spaces (also known as Iwaniec-Sbordone spaces) and grand Sobolev spaces. Namely, we prove a Kolmogorov-Riesz compactness theorem for grand Lebesgue spaces and the corresponding version of a result of Sudakov. In addition, the validity of a Rellich-Kondrachov type compact embedding is shown to hold in the context of grand Sobolev spaces.

Original language	English
Pages (from-to)	141-152
Number of pages	12
Journal	Georgian Mathematical Journal
Volume	22
Issue number	1
DOIs	https://doi.org/10.1515/gmj-2014-0060
Publication status	Published - Mar 1 2015
Externally published	Yes

Keywords

Grand Lebesgue spaces
Kolmogorov compactness
Rellich-Kondrachov compactness
grand Sobolev spaces

ASJC Scopus subject areas

General Mathematics

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10.1515/gmj-2014-0060

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KW - Rellich-Kondrachov compactness

KW - grand Sobolev spaces

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On the compactness in grand spaces

Abstract

Keywords

ASJC Scopus subject areas

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