Contents Online
Mathematical Research Letters
Volume 4 (1997)
Number 4
Hardy’s inequalities for Sobolev functions
Pages: 489 – 500
DOI: https://dx.doi.org/10.4310/MRL.1997.v4.n4.a6
Authors
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 $u\in W^{1,p}_0(\varOmega)$.
Published 1 January 1997