Approximation by double second type delayed arithmetic mean of periodic functions in $H_{p}^{(\omega, \omega)}$ space

TL;DR

This paper investigates how well functions in a specific function space can be approximated using double delayed arithmetic means of their Fourier series, with approximation quality expressed through moduli of continuity.

Contribution

It introduces new approximation estimates for functions in $H_{p}^{( au, au)}$ using second type double delayed arithmetic means of Fourier series, including more general even-type means.

Findings

Approximation degree expressed via moduli of continuity.

Results apply to second type double delayed arithmetic means.

Includes generalization to even-type means.

Abstract

In this paper, we give a degree of approximation of a function in the space $H_{p}^{(\omega, \omega)}$ by using the second type double delayed arithmetic means of its Fourier series. Such degree of approximation is expressed via two functions of moduli of continuity type. To obtain one more general result, we used the even-type double delayed arithmetic means of Fourier series as well.