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TWO-SIDED ESTIMATES OF THE LEBESGUE CONSTANTS WITH RESPECT TO VILENKIN SYSTEMS AND APPLICATIONS

Part of: Nontrigonometric harmonic analysis

Published online by Cambridge University Press:  13 March 2017

I. BLAHOTA ,
L. E. PERSSON  and
G. TEPHNADZE
I. BLAHOTA
Affiliation:
Institute of Mathematics and Computer Sciences, University of Nyíregyháza, P.O. Box 166, Nyíregyháza, H-4400, Hungary e-mail: blahota.istvan@nye.hu
L. E. PERSSON
Affiliation:
Department of Engineering Sciences and Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden UiT, The Artic University of Norway, P.O. Box 385, N-8505, Narvik, Norway e-mail: larserik@ltu.se
G. TEPHNADZE
Affiliation:
Department of Mathematics, Faculty of Exact and Natural Sciences, Tbilisi State University, Chavchavadze str. 1, Tbilisi 0128, Georgia Department of Engineering Sciences and Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden e-mail: giorgitephnadze@gmail.com
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Abstract

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In this paper, we derive two-sided estimates of the Lebesgue constants for bounded Vilenkin systems, we also present some applications of importance, e.g., we obtain a characterization for the boundedness of a subsequence of partial sums with respect to Vilenkin–Fourier series of H1 martingales in terms of n's variation. The conditions given in this paper are in a sense necessary and sufficient.

MSC classification

Primary: 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 1 , January 2018 , pp. 17 - 34
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

References

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