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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Dyadic-like maximal operators on integrable functions and Bellman functions related to Kolmogorov's inequality


Authors: Antonios D. Melas and Eleftherios Nikolidakis
Journal: Trans. Amer. Math. Soc. 362 (2010), 1571-1597
MSC (2000): Primary 42B25
Published electronically: October 20, 2009
MathSciNet review: 2563741
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Abstract: For each $ q<1$ we precisely evaluate the main Bellman functions associated with the behavior of dyadic maximal operators on $ \mathbb{R}^{n}$ on integrable functions. Actually we do that in the more general setting of tree-like maximal operators. These are related to and refine the corresponding Kolmogorov inequality, which we show is actually sharp. For this we use the effective linearization introduced by the first author in 2005 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 Athens, Panepistimiopolis 15784, Athens, Greece

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04872-7
PII: S 0002-9947(09)04872-7
Keywords: Bellman, dyadic, maximal
Received by editor(s): August 21, 2007
Received by editor(s) in revised form: April 7, 2008
Published electronically: October 20, 2009
Additional Notes: The authors were supported in part by the European Social Fund and National Resources-(EPEAK II) Pythagoras II
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.