The hardy-littlewood maximal function of a sobolev function |
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| Authors: | Juha Kinnunen |
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| Institution: | (1) Department of Mathematics, University of Helsinki, P.O. Box 4, FIN-00014, Finland |
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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. |
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| Keywords: | |
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