Sharp Sobolev inequalities in Lorentz spaces for a mean oscillation

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4 Citations (Scopus)

Abstract

We exhibit the optimal constant for Sobolev inequalities in Lorentz spaces for a mean oscillation, and its relation with a boundedness of the Hardy-Littlewood maximal operator in Sobolev spaces. Some applications to a scale invariant form of Hardy's inequality in a limiting case are also considered.

Original languageEnglish
Pages (from-to)2944-2958
Number of pages15
JournalJournal of Functional Analysis
Volume266
Issue number5
DOIs
Publication statusPublished - 2014 Mar 1
Externally publishedYes

Keywords

  • Critical Hardy inequalities
  • Optimal constant
  • Scale invariance property
  • Sobolev inequalities in Lorentz spaces

ASJC Scopus subject areas

  • Analysis

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