, Volume 100, Issue 1, pp 117-124

The hardy-littlewood maximal function of a sobolev function

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Abstract

We prove that the Hardy-Littlewood maximal operator is bounded in the Sobolev spaceW 1,p (R n ) for 1<p≤∞. As an application we study a weak type inequality for the Sobolev capacity. We also prove that the Hardy-Littlewood maximal function of a Sobolev function is quasi-continuous.