A counterexample to a weak-type estimate for potential spaces and tangential approach regions
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- by Javier Soria and Olof Svensson
- Proc. Amer. Math. Soc. 133 (2005), 1093-1099
- DOI: https://doi.org/10.1090/S0002-9939-04-07621-X
- Published electronically: September 16, 2004
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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.References
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Bibliographic Information
- Javier Soria
- Affiliation: Department of Applied Mathematics and Analysis, University of Barcelona, E-08071 Barcelona, Spain
- Email: soria@mat.ub.es
- Olof Svensson
- Affiliation: Department of Science and Technology, Campus Norrköping, Linköping University, SE-601 74 Norrköpingweden, Sweden
- Email: olosv@itn.liu.se
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 1093-1099
- MSC (2000): Primary 42B25, 42B20
- DOI: https://doi.org/10.1090/S0002-9939-04-07621-X
- MathSciNet review: 2117210