Resumen de Approximation by weighted means of cubical partial sums of double Walsh-Fourier series

Károly Nagy

• In this article we investigate the rate of the approximation by the weighted means of cubical partial sums of Walsh-Fourier series of a function in Lp (1 ≤ p ≤ ∞), in particular, in Lip(α, p) (for α > 0, 1 ≤ p ≤ ∞). In case p = ∞ by Lp we shall mean CW , the collection of the uniformly W-continuous functions. We show that the approximation behavior of the two-dimensional weighted means of Marcinkiewicz type is so good as the approximation behavior of the one-dimensional weighted means discussed by M´oricz and Rhoades.