Hardy inequalities and nonlocal capacity

Tomasz Grzywny; Julia Lenczewska

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arXiv · 2410.10001

Hardy inequalities and nonlocal capacity

Tomasz Grzywny·Julia Lenczewska

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Abstract

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 Hardy-type inequalities to obtain Sobolev embeddings and use them to estimate the nonlocal capacities of a ball.

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Tomasz Grzywny, Julia Lenczewska. 2024-10-13. Hardy inequalities and nonlocal capacity. https://arxiv.org/abs/2410.10001

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