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

15 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

Access to Document

10.1515/gmj-2014-0060

Cite this

@article{c7d1e632e1fd4385bfefdd96d8035a0d,

title = "On the compactness in grand spaces",

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.",

keywords = "Grand Lebesgue spaces, Kolmogorov compactness, Rellich-Kondrachov compactness, grand Sobolev spaces",

author = "Humberto Rafeiro and Andr{\'e}s Vargas",

note = "Publisher Copyright: {\textcopyright} 2015 Walter de Gruyter GmbH.",

year = "2015",

month = mar,

day = "1",

doi = "10.1515/gmj-2014-0060",

language = "English",

volume = "22",

pages = "141--152",

journal = "Georgian Mathematical Journal",

issn = "1072-947X",

publisher = "Plenum Publishers",

number = "1",

}

TY - JOUR

T1 - On the compactness in grand spaces

AU - Rafeiro, Humberto

AU - Vargas, Andrés

PY - 2015/3/1

Y1 - 2015/3/1

N2 - 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.

AB - 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.

KW - Grand Lebesgue spaces

KW - Kolmogorov compactness

KW - Rellich-Kondrachov compactness

KW - grand Sobolev spaces

UR - https://www.scopus.com/pages/publications/84925807787

UR - https://www.scopus.com/inward/citedby.url?scp=84925807787&partnerID=8YFLogxK

U2 - 10.1515/gmj-2014-0060

DO - 10.1515/gmj-2014-0060

M3 - Article

AN - SCOPUS:84925807787

SN - 1072-947X

VL - 22

SP - 141

EP - 152

JO - Georgian Mathematical Journal

JF - Georgian Mathematical Journal

IS - 1

ER -

On the compactness in grand spaces

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this