Mathematical Research Letters

Volume 4 (1997)

Number 4

Hardy’s inequalities for Sobolev functions

Pages: 489 – 500

DOI: http://dx.doi.org/10.4310/MRL.1997.v4.n4.a6

Authors

Juha Kinnunen

Olli Martio

Abstract

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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