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February 2018 On an approximation of 2-dimensional Walsh–Fourier series in martingale Hardy spaces
L. E. Persson, G. Tephnadze, P. Wall
Ann. Funct. Anal. 9(1): 137-150 (February 2018). DOI: 10.1215/20088752-2017-0032

Abstract

In this paper, we investigate convergence and divergence of partial sums with respect to the 2-dimensional Walsh system on the martingale Hardy spaces. In particular, we find some conditions for the modulus of continuity which provide convergence of partial sums of Walsh–Fourier series. We also show that these conditions are in a sense necessary and sufficient.

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L. E. Persson. G. Tephnadze. P. Wall. "On an approximation of 2-dimensional Walsh–Fourier series in martingale Hardy spaces." Ann. Funct. Anal. 9 (1) 137 - 150, February 2018. https://doi.org/10.1215/20088752-2017-0032

Information

Received: 29 November 2016; Accepted: 11 March 2017; Published: February 2018
First available in Project Euclid: 5 October 2017

zbMATH: 1382.42017
MathSciNet: MR3758749
Digital Object Identifier: 10.1215/20088752-2017-0032

Subjects:
Primary: 42C10
Secondary: 42B25

Keywords: 2-dimensional modulus of continuity , Fourier series , martingale Hardy space , strong summability , Walsh system

Rights: Copyright © 2018 Tusi Mathematical Research Group

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Vol.9 • No. 1 • February 2018
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