Approximation theorems for multivariate Taylor-Abel-Poisson means

Abstract

We obtain direct and inverse approximation theorems of functions of several variables by Taylor-Abel-Poisson means in the integral metrics. We also show that norms of multipliers in the spaces $L_{p,Y}(\mathbb T^d)$ are equivalent for all positive integers $d.$Comment: arXiv admin note: substantial text overlap with arXiv:1609.0961