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.