On the weighted maximal operators of Marcinkiewicz type Cesàro means of two-dimensional Walsh-Fourier series

Abstract

In this paper we investigate the behaviour of the weighted maximal operators of Marcinkiewicz type (C,?)-means ??,* p (f) := supn?P |??n(f)|/ n2/p?(2+?) in the Hardy space Hp(G2) (0 < ? < 1 and p < 2/(2 + ?)). It is showed that the maximal operators ??,* p (f) are bounded from the dyadic Hardy space Hp(G2) to the Lebesgue space Lp(G2), and that this is in a sense sharp. It was also proved a strong convergence theorem for the Marcinkiewicz type (C, ?) means of Walsh-Fourier series in Hp(G2).