On the two-dimensional Marcinkiewicz means with respect to Walsh-Kaczmarz system

Marcinkiewicz-Fejér means of double conjugate Walsh-Kaczmarz-Fourier series and Hardy spaces

In the present paper we prove that for any 0 < p ≤ 2/3 there exists a martingale f in Hp such that the Marcinkiewicz-Fejér means of double conjugate Walsh-Kaczmarz-Fourier series of the martingale f is not uniformly bounded in the space Lp .

On the Marcinkiewicz and (C, α)-means of the quadratical partial sums of double Walsh-Kaczmarz-Fourier series

On the Maximal Operators of Walsh-kaczmarz-nörlund Means

The main aim of this paper is to investigate (Hp, Lp,∞) type inequalities for maximal operators of Nörlund means with monotone coefficients of one-dimensional Walsh-Kaczmarz system. By applying this results we conclude a.e. convergence of such Walsh-Kaczmarz-Nörlund means.

Almost Everywhere Convergence of a Subsequence of the Nörlund Logarithmic Means of Walsh–kaczmarz–fourier Series

The main aim of this paper is to prove that the maximal operator of a subsequence of the (one-dimensional) logarithmic means of Walsh-Kaczmarz-Fourier series is of weak type (1,1) . Moreover, we prove that the maximal operator of the logarithmic means of quadratical partial sums of double Walsh-Kaczmarz-Fourier series is of weak type (1,1) , provided that the supremum in the maximal operator is...

On the L Norm of the Weighted Maximal Function of Fejér Kernels with Respect to the Walsh-kaczmarz System

The main aim of this paper is to investigate the integral of the weighted maximal function of the Walsh-Kaczmarz-Fejér kernels. We give a necessary and sufficient conditions for that the weighted maximal function of the Walsh-Kaczmarz-Fejér kernels is in L. After this we discuss the weighted maximal function of (C,α) kernels with respect to Walsh-Paley system too.