Communications
Mathematics

On the almost everywhere convergence of negative order Cesaro means of Fourier–Walsh series

L. N. Galoyan, R. G. Melikbekyan

Physical and Mathematical Faculty of Yerevan State University

Abstract: In the paper is presented existence of an increasing sequence of natural numbers $M_{\nu} (\nu=0,1,...)$, such that for any $\varepsilon>0$ there exists a measurable set $E$ with a measure $\mu E > 1-\varepsilon>0$ such that for any function $f(x)\in L^1[0, 1]$ one can find a function $g(x)\in L^1[0, 1]$ which coincides with the function $f$ on $E$, and for any a $\alpha\neq 1, 2,...$ the Cesaro means $\sigma^{\alpha}_{M_{\nu}} (x,\tilde{f})\ (\nu=0,1,...)$ converges to $g(x)$ almost everywhere on $[0,1]$.

Keywords: Fourier–Walsh series, Cesaro means.

MSC: Primary 42C10; Secondary 42B08

Received: 05.02.2016
Accepted: 25.02.2015

Language: English