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arXiv · 2002.11520

Self-improvement of weighted pointwise inequalities on open sets

Sylvester Eriksson-Bique·Juha Lehrbäck·Antti V. Vähäkangas
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Abstract

We prove a general self-improvement property for a family of weighted pointwise inequalities on open sets, including pointwise Hardy inequalities with distance weights. For this purpose we introduce and study the classes of $p$-Poincar\'e and $p$-Hardy weights for an open set $\Omega\subset X$, where $X$ is a metric measure space. We also apply the self-improvement of weighted pointwise Hardy inequalities in connection with usual integral versions of Hardy inequalities.

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Sylvester Eriksson-Bique, Juha Lehrbäck, Antti V. Vähäkangas. 2020-02-25. Self-improvement of weighted pointwise inequalities on open sets. https://arxiv.org/abs/2002.11520

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