Fractional hardy inequalities and visibility of the boundary

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

doi:10.4064/sm224-1-3

Fractional hardy inequalities and visibility of the boundary

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

Department of Mathematics and Systems Analysis

Research output: Contribution to journal › Article › Scientific › peer-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 language	English
Pages (from-to)	47-80
Number of pages	34
Journal	Studia Mathematica
Volume	224
Issue number	1
DOIs	https://doi.org/10.4064/sm224-1-3
Publication status	Published - 2014
MoE publication type	A1 Journal article-refereed

Keywords

Fractional hardy inequality
Hausdorff content
Uniform fatness
Visibility

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10.4064/sm224-1-3

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