Strong Approximation by Marcinkiewicz Means of two-dimensional Walsh-Kaczmarz-Fourier Series

Abstract

In this paper we study the exponential uniform strong approximation of Marcinkiewicz type of two-dimensional Walsh-Kaczmarz-Fourier series. In particular, it is proved that the Marcinkiewicz type of two-dimensional Walsh-Kaczmarz-Fourier series of the continuous function \(f\) is uniformly strong summable to the function \(f\) exponentially in the power \(1/2\). Moreover, it is proved that this result is best possible.