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 ${\mathbb R}^n$, $0 \lt s \lt 1$ and $1 \lt p \lt \infty$. As an application, we characterize the fractional $(s,p)$-Hardy inequality on a bounded open set by a Maz'ya-type testing condition localized to Whitney cubes.
Citation
Hannes LUIRO. Antti V. VÄHÄKANGAS. "Local maximal operators on fractional Sobolev spaces." J. Math. Soc. Japan 68 (3) 1357 - 1368, July, 2016. https://doi.org/10.2969/jmsj/06831357
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