Fractional hardy inequalities and visibility of the boundary

Lizaveta Ihnatsyeva, Juha Lehrbäck, Heli Tuominen, Antti V. Vähäkangas

Research output: Contribution to journalArticleScientificpeer-review

8 Citations (Scopus)

Abstract

We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditions alone are not sufficient for such Hardy inequalities to hold. In addition, we give a short exposition of various fatness conditions related to our main result, and apply fractional Hardy inequalities in connection with the boundedness of extension operators for fractional Sobolev spaces.

Original languageEnglish
Pages (from-to)47-80
Number of pages34
JournalStudia Mathematica
Volume224
Issue number1
DOIs
Publication statusPublished - 2014
MoE publication typeA1 Journal article-refereed

Keywords

  • Fractional hardy inequality
  • Hausdorff content
  • Uniform fatness
  • Visibility

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