The main aim of this paper is to investigate the Walsh-Marcinkiewicz means on the Hardy space H p, when 0 < p < 2/3. We define a weighted maximal operator of Walsh-Marcinkiewicz means and establish some of its properties. With its aid we provide a necessary and sufficient condition for convergence of the Walsh-Marcinkiewicz means in terms of modulus of continuity on the Hardy space H p, and prove a strong convergence theorem for the Walsh-Marcinkiewicz means.
@article{bwmeta1.element.doi-10_2478_s11533-014-0406-1,
author = {K\'aroly Nagy and George Tephnadze},
title = {Walsh-Marcinkiewicz means and Hardy spaces},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {1214-1228},
zbl = {1300.42003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-014-0406-1}
}
Károly Nagy; George Tephnadze. Walsh-Marcinkiewicz means and Hardy spaces. Open Mathematics, Tome 12 (2014) pp. 1214-1228. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-014-0406-1/
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