Dominated compactness theorem in banach function spaces and its applications

Humberto Rafeiro, Stefan Samko

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


A famous dominated compactness theorem due to Krasnosel'skiǐ states that compactness of a regular linear integral operator in Lp follows from that of a majorant operator. This theorem is extended to the case of the spaces Lp(ċ) (Ω, μ), μ Ω < ∞, with variable exponent p(•), where we also admit power type weights . This extension is obtained as a corollary to a more general similar dominated compactness theorem for arbitrary Banach function spaces for which the dual and associate spaces coincide. The result on compactness in the spaces Lp(ċ)(Ω, μ) is applied to fractional integral operators over bounded open sets.

Original languageEnglish
Pages (from-to)669-681
Number of pages13
JournalComplex Analysis and Operator Theory
Issue number4
Publication statusPublished - Dec 2008
Externally publishedYes


  • Banach function space
  • Compact majorant
  • Compact operators
  • Integral operator
  • Krasnoselskii theorem
  • Potential operator
  • Regular operator
  • Variable exponent Lebesgue space

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics


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