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

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

2003-09-04

arxiv.org/abs/math/0309063v1

Mathematics

Classical Analysis and ODEs

10 pages

Scientific paper

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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