Strong Summability of Two-Dimensional Vilenkin Fourier series

Abstract

In this paper we study the exponential uniform strong summability of two-dimensional Vilenkin-Fourier series. In particular, it is proved that the two-dimensional Vilenkin-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.

arXiv commentarXiv admin note: text overlap with arXiv:1609.01645