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

Authors: Javier Soria and Olof Svensson
Journal: Proc. Amer. Math. Soc. 133 (2005), 1093-1099
MSC (2000): Primary 42B25, 42B20
Published electronically: September 16, 2004
MathSciNet review: 2117210
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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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Additional Information

Javier Soria
Affiliation: Department of Applied Mathematics and Analysis, University of Barcelona, E-08071 Barcelona, Spain

Olof Svensson
Affiliation: Department of Science and Technology, Campus Norrköping, Linköping University, SE-601 74 Norrköpingweden, Sweden

Keywords: Potential spaces, maximal functions, approach regions.
Received by editor(s): June 7, 2003
Received by editor(s) in revised form: November 26, 2003
Published electronically: September 16, 2004
Additional Notes: The research of the first author was partially supported by Grants BFM2001-3395 and 2001SGR00069.
Communicated by: Andreas Seeger
Article copyright: © Copyright 2004 American Mathematical Society