D. M. D'yachenko, “Two-side estimates for sums of absolute values of Fourier coefficients of functions from <nobr>$H^\omega(T^m)$</nobr> with the use of partial moduli of smoothness”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2011, Number 1,Pages <nobr>3

Mathematics

Two-side estimates for sums of absolute values of Fourier coefficients of functions from $H^\omega(T^m)$ with the use of partial moduli of smoothness

D. M. D'yachenko

Financial analyst of the management company "Rosbank"

Abstract: Two-side estimates of sums of absolute values of Fourier coefficients for functions of many variables from the classes $H^\omega(T^m)$ are established in the paper with the help of partial moduli of smootness.

Key words: Fourier coefficients, partial moduli of smootness, Nikol'skii class.

UDC: 517.52

Received: 08.09.2009