We investigate convergence and divergence of specific subsequences of partial sums with respect to the Walsh system on martingale Hardy spaces. By using these results we obtain a relationship of the ratio of convergence of the partial sums of the Walsh series and the modulus of continuity of the martingale. These conditions are in a sense necessary and sufficient.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-2-7,
author = {George Tephnadze},
title = {On the partial sums of Walsh-Fourier series},
journal = {Colloquium Mathematicae},
volume = {139},
year = {2015},
pages = {227-242},
zbl = {1338.42040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-2-7}
}
George Tephnadze. On the partial sums of Walsh-Fourier series. Colloquium Mathematicae, Tome 139 (2015) pp. 227-242. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-2-7/