Fractional Hardy inequalities and visibility of the boundary

Lizaveta Ihnatsyeva, et al. "Fractional Hardy inequalities and visibility of the boundary." Studia Mathematica 224.1 (2014): 47-80. <http://eudml.org/doc/285574>.

@article{LizavetaIhnatsyeva2014,
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.},
author = {Lizaveta Ihnatsyeva, Juha Lehrbäck, Heli Tuominen, Antti V. Vähäkangas},
journal = {Studia Mathematica},
keywords = {fractional Hardy inequality; uniform fatness; visibility; Hausdorff content; extension operators; fractional Sobolev spaces},
language = {eng},
number = {1},
pages = {47-80},
title = {Fractional Hardy inequalities and visibility of the boundary},
url = {http://eudml.org/doc/285574},
volume = {224},
year = {2014},
}

TY - JOUR
AU - Lizaveta Ihnatsyeva
AU - Juha Lehrbäck
AU - Heli Tuominen
AU - Antti V. Vähäkangas
TI - Fractional Hardy inequalities and visibility of the boundary
JO - Studia Mathematica
PY - 2014
VL - 224
IS - 1
SP - 47
EP - 80
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.
LA - eng
KW - fractional Hardy inequality; uniform fatness; visibility; Hausdorff content; extension operators; fractional Sobolev spaces
UR - http://eudml.org/doc/285574
ER -