A maximal inequality for 𝐻¹-functions on a generalized Walsh-Paley group

Abstract

Abstract. Let G = n,°l0 Z(P¡) De me countable product of discrete cyclic groups of order p¡. We assume that sup/>0/>, < oo. We consider Walsh-

Strong convergence theorem for Vilenkin--Fejer means

“…. Since (see (5) and Lemma 2) (22) K Mn (x) = D Mn (x) = 0, for n ≥ 2 from ( 15) and ( 20)-( 21) we obtain that…”

“…The results for summability of Fejér means of Walsh-Fourier series can be found in [3,4,5], [8,9,10,11,12,13,14].…”

Strong convergence theorems for Walsh–Fejér means

“…The results for summability of Fejér means of Walsh-Fourier series can be found in [3,4], [7,8], [12], [14,16], [23,27].…”

Convergence of Ces\'{a}ro means with varying parameters of Walsh-Fourier series

“…For the sequence˛n D 1 Theorem 2 is due to Fujii [5]. For the more general but constant sequence˛n D˛1 see Weisz [11].…”