Approximation by Riesz Means of Hexagonal Fourier Series

Abstract

Let $f$ be an $H$-periodic (periodic with respect to the hexagon lattice) Hölder continuous function of two real variables. The error $\Vert f-R_n(p_k;f)\Vert$ is estimated in the uniform norm and in the Hölder norm, where $(p_k)$ is a sequence of numbers such that $0<p_0\le p_1\le \cdots$ and $R_n(p_k;f)$ is the $n$th Riesz mean of hexagonal Fourier series of $f$ with respect to $(p_k)$.