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Pointwise Hardy inequalities |
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| Authors: | Piotr Hajlasz |
| Affiliation: | Instytut Matematyki, Uniwersytet Warszawski, Banacha 2, 02--097 Warszawa, Poland |
| Abstract: | If  is an open set with the sufficiently regular boundary, then the Hardy inequality  holds for  and  , where  . The main result of the paper is a pointwise inequality  , where on the right hand side there is a kind of maximal function. The pointwise inequality combined with the Hardy-Littlewood maximal theorem implies the Hardy inequality. This generalizes some recent results of Lewis and Wannebo. |
| Keywords: | Hardy inequalities Sobolev spaces capacity $p$-thick sets maximal function Wiener criterion |
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