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-7094-79-04625-8 . [3] Hong , S. Taylor , P. Yang , C. W. 2006 Weak type estimates for maximal operators with a cylindric distance function

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Blahota, I., Gát, G. and Goginava, U. , Maximal operators of Fejér means of Vilenkin—Fourier series, JIPAM. J. Inequal. Pure Appl. Math ., 7 (2006), 1–7. Goginava U. Maximal

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Vilenkin systems , J. Approx. Theory , 124 ( 2003 ), no. 1 , 25 – 43 . [3] Goginava , U. , The maximal operator of the (C, α) means of the Walsh–Fourier series

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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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In this paper we prove that the maximal operator of the Marcinkiewicz-Fejér means of the 2-dimensional Vilenkin-Fourier series is not bounded from the Hardy space H 2/3 ( G 2 ) to the space L 2/3 ( G 2 ).

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Abstract  

The main aim of this paper is to prove that there exists a martingale fH 1 2/▭ such that the restricted maximal operators of Fejér means of twodimensional Walsh-Fourier series and conjugate Walsh-Fourier series does not belong to the space weak-L 1/2.

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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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Abstract  

The main aim of this paper is to prove that the maximal operator σ 0 k*:= supnσ n,n k∣ of the Fej�r means of double Fourier series with respect to the Kaczmarz system is not bounded from the Hardy space H 1/2 to the space weak-L 1/2.

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