Sharp local lower $L^{p}$-bounds for Dyadic-like maximal operators
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- by Antonios D. Melas, Eleftherios Nikolidakis and Theodoros Stavropoulos PDF
- Proc. Amer. Math. Soc. 141 (2013), 3171-3181 Request permission
Abstract:
We provide sharp lower $L^{p}$-bounds for the localized dyadic maximal operator on $\mathbb {R}^{n}$ when the local $L^{1}$ and the local $L^{p}$ norm of the function are given. We actually do that in the more general context of homogeneous trees in probability spaces. For this we use an effective linearization for such maximal operators on an adequate set of functions.References
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Additional Information
- Antonios D. Melas
- Affiliation: Department of Mathematics, University of Athens, Panepistimiopolis 15784, Athens, Greece
- MR Author ID: 311078
- Email: amelas@math.uoa.gr
- Eleftherios Nikolidakis
- Affiliation: Department of Mathematics, University of Crete, Knosou Boulevard, Herakleion, Crete, Greece
- MR Author ID: 850477
- Email: lefteris@math.uoc.gr
- Theodoros Stavropoulos
- Affiliation: Department of Mathematics, University of Athens, Panepistimiopolis 15784, Athens, Greece
- Email: tstavrop@math.uoa.gr
- Received by editor(s): November 27, 2011
- Published electronically: May 24, 2013
- Additional Notes: The authors were supported by research grant 70/4/7581 of the University of Athens
- Communicated by: Michael T. Lacey
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 3171-3181
- MSC (2010): Primary 42B25
- DOI: https://doi.org/10.1090/S0002-9939-2013-11789-2
- MathSciNet review: 3068970