On the order of the uniform convergence of partial cubic sums of multiple trigonometric Fourier series on the function classes $H_{1,m}^{l}[\omega]$

N. A. Il'yasov

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 4, pp. 161-177

Résumé

A solution of the problem on the exact order of deviation in the uniform metric of partial cubic sums of multiple trigonometric Fourier series on classes of functions with a given majorant for the total modulus of smoothness of the $l$th order in $L_1(\mathbb{T}^{m}) $ is presented, where $l\in \mathbb{N}$, $m\geq 1$.

Détail

Keywords: multiple trigonometric Fourier series, partial cubic sums, order of uniform convergence, total modulus of smoothness, exact order of deviation in the uniform metric.

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