4 citations · 4 across the 5 of their papers we have counts for
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Hardy inequalities and nonlocal capacity
Tomasz Grzywny, Julia Lenczewska
In this article, we introduce and study capacities related to nonlocal Sobolev spaces, with focus on spaces corresponding to zero-order nonlocal operators. In particular, we prove…
Asymptotics and geometric flows for a class of nonlocal curvatures
Wojciech Cygan, Tomasz Grzywny, Julia Lenczewska
We consider a family of nonlocal curvatures determined through a kernel which is symmetric and bounded from above by a radial and radially non-increasing profile satisfying an inte…
Sharp Hardy inequalities for Sobolev-Bregman forms
Michał Kijaczko, Julia Lenczewska
We obtain sharp fractional Hardy inequalities for the half-space and for convex domains. We extend the results of Bogdan and Dyda and of Loss and Sloane to the setting of Sobolev-B…
Optimal Hardy inequality for the fractional Laplacian on
Krzysztof Bogdan, Tomasz Jakubowski, Julia Lenczewska +1
For the fractional Laplacian we give Hardy inequality which is optimal in for . As an application, we explicitly characterize the contractivity of the correspondi…