We investigate the bounded Ciesielski systems, which can be obtained from the spline systems of order (m,k) in the same way as the Walsh system arises from the Haar system. It is shown that the maximal operator of the Fejér means of the Ciesielski-Fourier series is bounded from the Hardy space to if 1/2 < p < ∞ and m ≥ 0, |k| ≤ m + 1. Moreover, it is of weak type (1,1). As a consequence, the Fejér means of the Ciesielski-Fourier series of a function f converges to f a.e. if f ∈ L₁ as n → ∞.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-3-2,
author = {Ferenc Weisz},
title = {On the Fej\'er means of bounded Ciesielski systems},
journal = {Studia Mathematica},
volume = {147},
year = {2001},
pages = {227-243},
zbl = {0988.46003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-3-2}
}
Ferenc Weisz. On the Fejér means of bounded Ciesielski systems. Studia Mathematica, Tome 147 (2001) pp. 227-243. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm146-3-2/