The Hardy-Littlewood maximal function of a Sobolev function
In this paper a main result is that the Hardy-Littlewood maximal operator is bounded in the Sobolev space \(W^{1,p}(\mathbb{R}^n)\) for \(1<p\leq\infty\). This result is applied to study a weak type inequality for the Sobolev capacity and to prove that the Hardy-Littlewood maximal function of a Sobolev function is quasi-continuous.
scientific article; zbMATH DE number 1062358