Mathematical Research Letters

Volume 4, Issue 4, July 1997 pp. 489-500.

Hardy's inequalities for Sobolev functions

Authors: Juha Kinnunen and Olli Martio
Author institution: University of Helsinki

Summary: The fractional maximal function of the gradient gives a pointwise interpretation of Hardy's inequality for functions $u\in W^{1,p}_0(\varOmega)$. With mild assumptions on $\varOmega$ Hardy's inequality holds for a function $u\in W^{1,p}(\varOmega)$ if and only if $u\in W^{1,p}_0(\varOmega)$.

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