Approximation on hexagonal domains by Taylor-Abel-Poisson means

Approximative properties of the Taylor-Abel-Poisson linear summation method of Fourier series are considered for functions of several variables, periodic with respect to the hexagonal domain, in the integral metric. In particular, direct and inverse theorems are proved in terms of approximations of functions by the Taylor-Abel-Poisson means and K-functionals generated by radial derivatives. Bernstein type inequalities for L1-norm of radial derivatives of arbitrary order of the Poisson kernel are also obtained.(c) 2023 Elsevier Inc. All rights reserved.