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

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

On the Uniform Convergence and L-convergence of Double Fourier Series with Respect to the Walsh–kaczmarz System

In this paper we study the approximation by rectangular partial sums of a double Fourier series with respect to the Walsh–Kaczmarz system in the spaces C and L. From our results we obtain different criteria of the uniform convergence and L-convergence of a double Fourier–Kaczmarz series. 2000 Mathematics Subject Classification: Primary 41A50; Secondary 42C10.

Summation of Fourier Series

A general summability method of different orthogonal series is given with the help of an integrable function θ. As special cases the trigonometric Fourier, Walsh-, Walsh-Kaczmarz-, Vilenkinand Ciesielski-Fourier series and the Fourier transforms are considered. For each orthonormal system a different Hardy space is introduced and the atomic decomposition of these Hardy spaces are presented. A s...

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...

MAXIMAL OPERATORS OF THE FEJÉR MEANS OF THE TWO DIMENSIONAL CHARACTER SYSTEM OF THE p-SERIES FIELD IN THE KACZMARZ REARRANGEMENT

The main aim of this paper is to prove that the maximal operator σ∗ of the Fejér means of the two dimensional character system of the p-series field in the Kaczmarz rearrangement is bounded from the Hardy space Hα to the space Lα for α > 1/2, provided that the supremum in the maximal operator is taken over a positive cone. We also prove that the maximal operator σ∗ 0 of Fejér means of the two d...