# Approximation theorems for multivariate Taylor-Abel-Poisson means

## TL;DR

This paper establishes approximation theorems for multivariate functions using Taylor-Abel-Poisson means in integral metrics, and demonstrates the equivalence of multiplier norms across different dimensions.

## Contribution

It provides new direct and inverse approximation theorems for multivariate functions and shows norm equivalence of multipliers in $L_{p,Y}(\

## Key findings

- Established approximation theorems for multivariate functions.
- Proved norm equivalence of multipliers across dimensions.
- Extended classical approximation results to multivariate settings.

## 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 $d.$