English

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

Classical Analysis and ODEs 2007-05-23 v1

Abstract

We show that for every nontrivial potential space LK1(Rn)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.

Keywords

Cite

@article{arxiv.math/0309063,
  title  = {A counterexample to a weak-type estimate for potential spaces and tangential approach regions},
  author = {Javier Soria and Olof Svensson},
  journal= {arXiv preprint arXiv:math/0309063},
  year   = {2007}
}

Comments

10 pages

R2 v1 2026-07-22T16:57:22.729Z