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

Javier Soria·Olof Svensson
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Abstract

We show that for every nontrivial 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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Javier Soria, Olof Svensson. 2003-09-04. A counterexample to a weak-type estimate for potential spaces and tangential approach regions. https://arxiv.org/abs/math/0309063

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