Annals of Functional Analysis

On an approximation of 2-dimensional Walsh–Fourier series in martingale Hardy spaces

L. E. Persson, G. Tephnadze, and P. Wall

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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.

Article information

Ann. Funct. Anal. Volume 9, Number 1 (2018), 137-150.

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

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Digital Object Identifier

Primary: 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
Secondary: 42B25: Maximal functions, Littlewood-Paley theory

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


Persson, L. E.; Tephnadze, G.; Wall, P. On an approximation of $2$ -dimensional Walsh–Fourier series in martingale Hardy spaces. Ann. Funct. Anal. 9 (2018), no. 1, 137--150. doi:10.1215/20088752-2017-0032.

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