Approximation by Marcinkiewicz ϴ-means of double Walsh-Fourier series

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 .

Approximation 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....

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

On the Approximation Properties of Cesàro Means of Negative Order of Walsh-Fourier Series

In this paper we establish approximate properties of Cesàro (C,−α)-means with α ∈ (0, 1) of Walsh-Fourier series. This result allows one to obtain the condition which is sufficient for the convergence of the means σ−α n (f, x) to f (x) in the L p-metric. We also show that this condition cannot be improved in the case p = 1.

Maximal Operators of Fejér Means of Walsh–fourier Series

The main aim of this paper is to prove that there exists a martingale f ∈ H1/2 such that the maximal Fejér operator and the conjugate Fejér operator does not belong to the space L1/2.