The hardy-littlewood maximal function of a sobolev function
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We prove that the Hardy-Littlewood maximal operator is bounded in the Sobolev spaceW1,p(Rn) 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.
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- E. M. Stein,Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1970.Google Scholar