A counterexample to a weak-type estimate for potential spaces and tangential approach regions

Soria, Javier; Svensson, Olof

doi:10.1090/S0002-9939-04-07621-X

A counterexample to a weak-type estimate for potential spaces and tangential approach regions
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by Javier Soria and Olof Svensson PDF

Proc. Amer. Math. Soc. 133 (2005), 1093-1099 Request permission

Abstract:

We show that for every potential space $L^{1}_{K}(\mathbb {R}^{n})$, there exists an approach region for which the associated maximal function is of weak-type, but the boundedness for the completed region is false, which is in contrast with the nontangential case.

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