3 papers
math.AP2024
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…
math.AP2023
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…
math.AP2021
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…