Geodesic
Fractional Hardy inequalities and visibility of the boundary
Lizaveta Ihnatsyeva 1   ; Juha Lehrbäck 2   ; Heli Tuominen 2   ; Antti V. Vähäkangas 3
1 Department of Mathematics and Systems Analysis Aalto University P.O. Box 11100 FI-00076 Aalto, Finland and Department of Mathematics and Statistics University of Jyväskylä P.O. Box 35 (MaD) FI-40014 University of Jyväskylä, Finland
2 Department of Mathematics and Statistics University of Jyväskylä P.O. Box 35 (MaD) FI-40014 University of Jyväskylä, Finland
3 Department of Mathematics and Statistics University of Helsinki P.O. Box 68 FI-00014 University of Helsinki, Finland and Department of Mathematics and Statistics University of Jyväskylä P.O. Box 35 (MaD) FI-40014 University of Jyväskylä, Finland
Studia Mathematica, Tome 224 (2014) no. 1, pp. 47-80 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm224-1-3
Keywords: prove fractional order hardy inequalities sets under combined fatness visibility condition boundary demonstrate counterexamples fatness conditions alone sufficient hardy inequalities addition short exposition various fatness conditions related main result apply fractional hardy inequalities connection boundedness extension operators fractional sobolev spaces

Lizaveta Ihnatsyeva  1   ; Juha Lehrbäck  2   ; Heli Tuominen  2   ; Antti V. Vähäkangas  3

1 Department of Mathematics and Systems Analysis Aalto University P.O. Box 11100 FI-00076 Aalto, Finland and Department of Mathematics and Statistics University of Jyväskylä P.O. Box 35 (MaD) FI-40014 University of Jyväskylä, Finland
2 Department of Mathematics and Statistics University of Jyväskylä P.O. Box 35 (MaD) FI-40014 University of Jyväskylä, Finland
3 Department of Mathematics and Statistics University of Helsinki P.O. Box 68 FI-00014 University of Helsinki, Finland and Department of Mathematics and Statistics University of Jyväskylä P.O. Box 35 (MaD) FI-40014 University of Jyväskylä, Finland 
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Lizaveta Ihnatsyeva; Juha Lehrbäck; Heli Tuominen; Antti V. Vähäkangas. Fractional Hardy inequalities and visibility of the boundary. Studia Mathematica, Tome 224 (2014) no. 1, pp. 47-80. doi: 10.4064/sm224-1-3

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