Fractional hardy inequalities and visibility of the boundary

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Fractional hardy inequalities and visibility of the boundary. / Ihnatsyeva, Lizaveta; Lehrbäck, Juha; Tuominen, Heli; Vähäkangas, Antti V.

In: Studia Mathematica, Vol. 224, No. 1, 2014, p. 47-80.

Research output: Contribution to journalArticleScientificpeer-review

Harvard

Ihnatsyeva, L, Lehrbäck, J, Tuominen, H & Vähäkangas, AV 2014, 'Fractional hardy inequalities and visibility of the boundary' Studia Mathematica, vol. 224, no. 1, pp. 47-80. https://doi.org/10.4064/sm224-1-3

APA

Ihnatsyeva, L., Lehrbäck, J., Tuominen, H., & Vähäkangas, A. V. (2014). Fractional hardy inequalities and visibility of the boundary. Studia Mathematica, 224(1), 47-80. https://doi.org/10.4064/sm224-1-3

Vancouver

Ihnatsyeva L, Lehrbäck J, Tuominen H, Vähäkangas AV. Fractional hardy inequalities and visibility of the boundary. Studia Mathematica. 2014;224(1):47-80. https://doi.org/10.4064/sm224-1-3

Author

Ihnatsyeva, Lizaveta ; Lehrbäck, Juha ; Tuominen, Heli ; Vähäkangas, Antti V. / Fractional hardy inequalities and visibility of the boundary. In: Studia Mathematica. 2014 ; Vol. 224, No. 1. pp. 47-80.

Bibtex - Download

@article{04cb2a28ce5b4c8eb14937464cabea91,
title = "Fractional hardy inequalities and visibility of the boundary",
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.",
keywords = "Fractional hardy inequality, Hausdorff content, Uniform fatness, Visibility",
author = "Lizaveta Ihnatsyeva and Juha Lehrb{\"a}ck and Heli Tuominen and V{\"a}h{\"a}kangas, {Antti V.}",
year = "2014",
doi = "10.4064/sm224-1-3",
language = "English",
volume = "224",
pages = "47--80",
journal = "Studia Mathematica",
issn = "0039-3223",
publisher = "Instytut Matematyczny",
number = "1",

}

RIS - Download

TY - JOUR

T1 - Fractional hardy inequalities and visibility of the boundary

AU - Ihnatsyeva, Lizaveta

AU - Lehrbäck, Juha

AU - Tuominen, Heli

AU - Vähäkangas, Antti V.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Fractional hardy inequality

KW - Hausdorff content

KW - Uniform fatness

KW - Visibility

UR - http://www.scopus.com/inward/record.url?scp=84918576744&partnerID=8YFLogxK

U2 - 10.4064/sm224-1-3

DO - 10.4064/sm224-1-3

M3 - Article

VL - 224

SP - 47

EP - 80

JO - Studia Mathematica

JF - Studia Mathematica

SN - 0039-3223

IS - 1

ER -

ID: 12919564