Approximation by riesz means of hexagonal fourier series

Abstract

Let f be an H-periodic (periodic with respect to the hexagon lattice) Holder continuous function of two real variables. The error vertical bar vertical bar f-R-n (pk; f)vertical bar vertical bar is estimated in the uniform norm and in the Holder norm, where (pk) is a sequence of numbers such that 0 < p(0) <= p(1) <= ... and R-n (p(k); f) is the nth Riesz mean of hexagonal Fourier series of f with respect to (p(k)).