Journal of the Mathematical Society of Japan

Local maximal operators on fractional Sobolev spaces

Hannes LUIRO and Antti V. VÄHÄKANGAS

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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.

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J. Math. Soc. Japan Volume 68, Number 3 (2016), 1357-1368.

First available in Project Euclid: 19 July 2016

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Zentralblatt MATH identifier

Primary: 42B25: Maximal functions, Littlewood-Paley theory
Secondary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems 47H99: None of the above, but in this section

local maximal operator fractional Sobolev space Hardy inequality


LUIRO, Hannes; VÄHÄKANGAS, Antti V. Local maximal operators on fractional Sobolev spaces. J. Math. Soc. Japan 68 (2016), no. 3, 1357--1368. doi:10.2969/jmsj/06831357.

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