Continuity of the maximal operator in Sobolev spaces

Luiro, Hannes

doi:10.1090/S0002-9939-06-08455-3

Continuity of the maximal operator in Sobolev spaces
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by Hannes Luiro PDF

Proc. Amer. Math. Soc. 135 (2007), 243-251 Request permission

Abstract:

We establish the continuity of the Hardy-Littlewood maximal operator on Sobolev spaces $W^{1,p}(\mathbb {R}^n)$, $1<p<\infty$. As an auxiliary tool we prove an explicit formula for the derivative of the maximal function.

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