Weak type inequalityy for the maximal operator of the \((C,\alpha)\) means of two-dimensional Walsh-Fourier series
type: Item
instance of: scholarly article
title: Weak type inequalityy for the maximal operator of the \((C,\alpha)\) means of two-dimensional Walsh-Fourier series
zbMATH Open document ID: 1240.42127
author: Ushangi Goginava
published in: Analysis Mathematica
publication date: 2011-07-22T00:00:00Z
review text: It is known that the maximal operator \(\sigma_*^1\) of the Fejér means of the cubical partial sums \(S_{j,j}f\) of the two-dimensional Walsh-Fourier series of \(f\) is bounded from \(H_p\) to \(L_p\) if \(2/3<p<\infty\) (see \textit{F. Weisz} [Approximation Theory Appl. 17, No. ~2, 32--44 (2001; Zbl 0992.42013)]). Moreover, \textit{U. Goginava} [Anal. Math. 33, No. ~4, 263--286 (2007)] proved that the maximal Cesàro operator \(\sigma_*^\alpha\) \((0<\alpha<1)\) is bounded from \(H_p\) to \(L_p\) when \(2/(2+\alpha)<p<\infty\) and it is not bounded when \(0<p\leq 2/(2+\alpha)\). In this paper it is shown for the critical index \(p=2/(2+\alpha)\) that \(\sigma_*^\alpha\) is bounded from \(H_p\) to the weak \(L_p\) space.
Mathematics Subject Classification ID: 42C10
Mathematics Subject Classification ID: 43A75
Mathematics Subject Classification ID: 60G42
Mathematics Subject Classification ID: 42B30
zbMATH DE Number: 5931409
zbMATH Keywords: Walsh-Fourier series
zbMATH Keywords: cubical partial sums
zbMATH Keywords: Cesàro summability
zbMATH Keywords: Hardy spaces, atoms
reviewed by: Ferenc Weisz
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5931409