  Approximative properties of the Taylor-Abel-Poisson linear summation me\-thod
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 $L_1$-norm of high-order radial
derivatives of the Poisson kernel are also obtained.
