Israel Journal of Mathematics

, Volume 100, Issue 1, pp 117–124

The hardy-littlewood maximal function of a sobolev function


DOI: 10.1007/BF02773636

Cite this article as:
Kinnunen, J. Isr. J. Math. (1997) 100: 117. doi:10.1007/BF02773636


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.

Copyright information

© Hebrew University 1997

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of HelsinkiFinland