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 Lp,Y (T d ) are equivalent for all positive integers d. (2010): 41A27, 42A45, 41A35. Mathematics Subject Classification

Approximation on hexagonal domains by Taylor-Abel-Poisson means

“…First, let us give some auxiliary results. The proofs are similar to those of Lemmas 3.6-3.8 in [20].…”

“…In the proof of the Theorems 3.2 and 3.3, we mainly use the scheme from [21], [19] and [20] modifying it in due consideration of the peculiarities of the spaces L p (Ω). First, let us give some auxiliary results.…”

“…In the integral metrics, for 2π-periodic functions and for functions of several variables 2πperiodic in each variable, direct and inverse theorems of approximation by the operators A ̺,r were given in the terms of K-functionals of functions generated by their radial derivatives in [19] and [20] respectively.…”