Conditions of absolute Cesaro summability of multiple trigonometric Fourier series

Abstract

A necessary and sufficient condition of absolute |C; β|λ-summability almost everywhere on Ts is obtained for multiple trigonometric Fourier series of functions f ∈ Lq(Ts) from generalized Besov classes Bq,s,θ ωr , where Ts = [0, 2π)s, β = (β1, β2, . . ., βs), q = (q1, q2, . . ., qs), 1 < qj ≤ 2, j = 1, s, 1 ≤ λ ≤ qs ≤ . . . ≤ q1, λ < θ < ∞, 0 ≤ βj < 1/qj ′ = 1 − 1/qj, j = 1, s, r ∈ N, r > Ps j=1(1/qj − βj), and ωr is a function of the type of modulus of smoothness of order r. © 2019 Krasovskii Institute of Mathematics and Mechanics. All Rights Reserved.