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arXiv · 1406.1637

Local maximal operators on fractional Sobolev spaces

Hannes Luiro·Antti V. Vähäkangas
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Abstract

In this note we establish the boundedness properties of local maximal operators $M_G$ on the fractional Sobolev spaces $W^{s,p}(G)$ whenever $G$ is an open set in $\mathbb{R}^n$, $0<s<1$ and $1<p<\infty$. As an application, we characterize the fractional $(s,p)$-Hardy inequality on a bounded open set $G$ by a Maz'ya-type testing condition localized to Whitney cubes.

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Hannes Luiro, Antti V. Vähäkangas. 2014-06-06. Local maximal operators on fractional Sobolev spaces. https://arxiv.org/abs/1406.1637

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