On the Marcinkiewicz and (C, α)-means of the quadratical partial sums of double Walsh-Kaczmarz-Fourier series
نویسندگان
چکیده
منابع مشابه
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...
متن کاملMarcinkiewicz-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 .
متن کاملOn 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.
متن کاملApproximation by Nörlund Means of Double Walsh–fourier Series for Lipschitz Functions
For double trigonometric Fourier series, Móricz and Rhoades studied the rate of uniform approximation by Nörlund means of the rectangular partial sums of double Fourier series of a function belonging to the class Lipα (0 < α 1) [12] and the class of continuous functions [13], on the two-dimensional torus. As a special case, they obtained the rate of uniform approximation by double Cesàro means....
متن کاملAlmost Everywhere Convergence of a Subsequence of the Logarithmic Means of Vilenkin-Fourier Series
Abstract: The main aim of this paper is to prove that the maximal operator of a subsequence of the (one-dimensional) logarithmic means of Vilenkin-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 Vilenkin-Fourier series is of weak type (1,1), provided that the supremum in the maximal operator is tak...
متن کامل