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Fractional Hardy inequalities and visibility of the boundary

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Ihnatsyeva L., Lehrbäck J., Tuominen H., Vähäkangas A.

Studia Mathematica

2014

tom 224

nr 1

47-80

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.

Ograniczanie wyników

1 Studia Mathematica

1 Ihnatsyeva L.

1 Lehrbäck J.

1 Tuominen H.

1 Vähäkangas A.

1 2014

Wyniki wyszukiwania

Fractional Hardy inequalities and visibility of the boundary