Fractional hardy inequalities and visibility of the boundary

Research output: Contribution to journalArticleScientificpeer-review

Details

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

Researchers

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

Research units

  • University of Jyväskylä
  • University of Helsinki

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.

    Research areas

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

ID: 12919564