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The main aim of this paper is to prove that the maximal operator σ of the Marcinkiewicz–Fejér means of the two-dimensional Walsh–Fourier series is bounded from the Hardy space H2/3 to the space weak-L2/3. c © 2008 Elsevier Inc. All rights reserved.
In this paper we prove that the maximal operator of the subsequence of logarithmic means of Walsh-Fourier series is weak type (1,1). Moreover, the logarithmic means tmn (f) of the function f ∈ L converge a.e. to f as n →∞. In the literature, it is known the notion of the Riesz’s logarithmic means of a Fourier series. The n-th mean of the Fourier series of… (More)
It is proved that the maximal operator σ # of the triangular-Fejér-means of a two-dimensional Walsh–Fourier series is bounded from the dyadic Hardy space Hp to Lp for all 1/2 < p ≤ ∞ and, consequently, is of weak type (1,1). As a consequence we obtain that the triangular-Fejér-means σ 2n of a function f ∈ L1 converge a.e. to f . The maximal operator σ # is… (More)
The main aim of this paper is to prove that the maximal operator σ∗ := sup n |σn| of the Fejér means of the Vilenkin-Fourier series is not bounded from the Hardy space H1/2 to the space L1/2.
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… (More)
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… (More)