Approximation of continuous functions by de la Vallée-Poussin means of Fourier series on hexagonal domains

Abstract

For a Hölder continuous function f, periodic with respect to the hexagon lattice, deviations of generalized de la Vallée-Poussin means Vλn (f) and classical de la Vallée-Poussin means Vn2n (f) of its hexagonal Fourier series from f are estimated in uniform and Hölder norms.