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  • Author or Editor: U. Goginava x
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Abstract  

The aim of this paper is to prove that for an arbitrary set of measure zero there exists a bounded function for which the Fejér means of the Walsh-Fourier series of the function diverge.

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Abstract  

The main aim of this paper is to prove that the maximal operator
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\sigma _0^* : = \mathop {\sup }\limits_n \left| {\sigma _{n,n} } \right|$$ \end{document}
of the Fejr mean of the double Walsh-Fourier series is not bounded from the Hardy space H 1/2 to the space weak-L 1/2.
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Abstract  

We study the uniform convergence of Walsh-Fourier series of functions on the generalized Wiener class BV (p(n)↑∞)

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Abstract  

Simon [12] proved that the maximal operator of (C, α)-means of Fourier series with respect to the Walsh-Kaczmarz system is bounded from the martingale Hardy space H p to the space L p for p > 1/(1 + α). In this paper we prove that this boundedness result does not hold if p ≦ 1/(1 + α). However, in the endpoint case p = 1/(1 + α) the maximal operator σ * α,k is bounded from the martingale Hardy space H 1/(1+α) to the space weak-L 1/(1+α).

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