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arXiv · 0709.2013

Equivalence and self-improvement of p-fatness and Hardy's inequality, and association with uniform perfectness

Riikka Korte·Nageswari Shanmugalingam
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Abstract

We present an easy proof that $p$--Hardy's inequality implies uniform $p$--fatness of the boundary when $p=n$. The proof works also in metric space setting and demonstrates the self--improving phenomenon of the $p$--fatness. We also explore the relationship between $p$-fatness, $p$-Hardy inequality, and the uniform perfectness for all $p\ge 1$, and demonstrate that in the Ahlfors $Q$-regular metric measure space setting with $p=Q$, these three properties are equivalent.

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Riikka Korte, Nageswari Shanmugalingam. 2008-01-14. Equivalence and self-improvement of p-fatness and Hardy's inequality, and association with uniform perfectness. https://doi.org/10.1007/s00209-008-0454-y

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