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Sharp local lower $ L^{p}$-bounds for Dyadic-like maximal operators


Authors: Antonios D. Melas, Eleftherios Nikolidakis and Theodoros Stavropoulos
Journal: Proc. Amer. Math. Soc. 141 (2013), 3171-3181
MSC (2010): Primary 42B25
DOI: https://doi.org/10.1090/S0002-9939-2013-11789-2
Published electronically: May 24, 2013
MathSciNet review: 3068970
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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.


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Additional Information

Antonios D. Melas
Affiliation: Department of Mathematics, University of Athens, Panepistimiopolis 15784, Athens, Greece
Email: amelas@math.uoa.gr

Eleftherios Nikolidakis
Affiliation: Department of Mathematics, University of Crete, Knosou Boulevard, Herakleion, Crete, Greece
Email: lefteris@math.uoc.gr

Theodoros Stavropoulos
Affiliation: Department of Mathematics, University of Athens, Panepistimiopolis 15784, Athens, Greece
Email: tstavrop@math.uoa.gr

DOI: https://doi.org/10.1090/S0002-9939-2013-11789-2
Keywords: Bellman, dyadic, maximal
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
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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