# On estimates of deviation of conjugate functions from matrix operators of their Fourier series by some expressions with $r$-differences of the entries

## TL;DR

This paper extends previous results on the deviation of conjugate functions from matrix operators of Fourier series, providing new estimates involving $r$-differences of matrix entries.

## Contribution

It introduces novel bounds for conjugate Fourier series deviations using $r$-differences, expanding prior work to conjugate series cases.

## Key findings

- Extended deviation estimates to conjugate Fourier series.
- Derived bounds involving $r$-differences of matrix entries.
- Generalized previous results to broader classes of Fourier series.

## Abstract

We extend the results of the authors from [Abstract and Applied Analysis, Volume 2016, Article ID 9712878] to the case conjugate Fourier series.