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arXiv · 2108.07209

Fractional Poincar\'e and localized Hardy inequalities on metric spaces

Bartłomiej Dyda·Juha Lehrbäck·Antti V. Vähäkangas
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Abstract

We prove fractional Sobolev-Poincar\'e inequalities, capacitary versions of fractional Poincar\'e inequalities, and pointwise and localized fractional Hardy inequalities in a metric space equipped with a doubling measure. Our results generalize and extend earlier work where such inequalities have been considered in the Euclidean spaces or in the non-fractional setting in metric spaces. The results concerning pointwise and localized variants of fractional Hardy inequalities are new even in the Euclidean case.

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Bartłomiej Dyda, Juha Lehrbäck, Antti V. Vähäkangas. 2021-08-16. Fractional Poincar\'e and localized Hardy inequalities on metric spaces. https://arxiv.org/abs/2108.07209

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