# Estimates of convolution operators of functions from $L_{2\pi}^{p(x)}$

## TL;DR

This paper extends previous results on convolution operators acting on functions with variable exponent Lebesgue spaces, providing slight improvements and applications to the de la Vallée Poussin operator.

## Contribution

It generalizes and slightly improves earlier work on convolution operators in variable exponent Lebesgue spaces, with new applications to approximation operators.

## Key findings

- Improved bounds for convolution operators in $L_{2 ext{-}pi}^{p(x)}$ spaces.
- Applications demonstrated for the de la Vallée Poussin operator.
- Enhanced understanding of approximation in variable exponent spaces.

## Abstract

We generalize and slight improve the result of I. I. Sharapudinov [Mat. Zametki, 1996, Volume 59, Issue 2, 291--302]. Some applications to the de la Vall\'{e}e Poussin operator will also be given.