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Analysis demonstrates Hardy-type inequalities and estimates of nonlocal capacities in Sobolev spaces, suggesting new insights into nonlocal operators.
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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Grzywny et al. (2025) studied this question.
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