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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Extremal sequences for the Bellman function of three variables of the dyadic maximal operator related to Kolmogorov's inequality


Author: Eleftherios N. Nikolidakis
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 42B25; Secondary 42B99
DOI: https://doi.org/10.1090/tran/7843
Published electronically: May 31, 2019
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Abstract: We give a characterization of the extremal sequences for the Bellman function of three variables of the dyadic maximal operator in relation to Kolmogorov's inequality. In fact we prove that they behave approximately like eigenfunctions of this operator for a specific eigenvalue. For this approach we use the one introduced in a paper by A. D. Melas and the author, where the respective Bellman function has been precisely evaluated.


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Additional Information

Eleftherios N. Nikolidakis
Affiliation: Department of Mathematics, Panepistimiopolis, University of Ioannina, Ioannina 45110, Greece
Email: enikolid@uoi.gr

DOI: https://doi.org/10.1090/tran/7843
Received by editor(s): December 12, 2017
Received by editor(s) in revised form: December 12, 2018
Published electronically: May 31, 2019
Article copyright: © Copyright 2019 American Mathematical Society