On the compactness in grand spaces

Humberto Rafeiro, Andrés Vargas

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


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 languageEnglish
Pages (from-to)141-152
Number of pages12
JournalGeorgian Mathematical Journal
Issue number1
Publication statusPublished - Mar 1 2015
Externally publishedYes


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

ASJC Scopus subject areas

  • General Mathematics


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