# Some inequalities for Ces\`aro Means of double Vilenkin-Fourier Series

## TL;DR

This paper establishes new inequalities that describe how well Cesàro means approximate functions in the $L^p$ space using double Vilenkin-Fourier series, enhancing understanding of convergence rates.

## Contribution

It introduces novel inequalities that relate to the approximation rate of Cesàro means for double Vilenkin-Fourier series in $L^p$ spaces, advancing theoretical knowledge.

## Key findings

- New inequalities for Cesàro means approximation rates
- Improved understanding of convergence in $L^p$ spaces
- Enhanced bounds for double Vilenkin-Fourier series

## Abstract

In this paper we state and prove some new inequalities related to the rate of $L^{p}$ approximation by Ces\`aro means of the quadratic partial sums of double Vilenkin-Fourier series of functions from $L^{p}$.