Israel Journal of Mathematics

, Volume 100, Issue 1, pp 117–124 | Cite as

The hardy-littlewood maximal function of a sobolev function

Article

Abstract

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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Copyright information

© Hebrew University 1997

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of HelsinkiFinland

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