A note on estimates for the growth order of sequences of multiple rectangular Fourier sums

Abstract

Let {S nk(f,x)} ∞ k=1 be some sequence of rectangular partial sums of the multiple trigonometric Fourier series of a function f, and let {λ k} k=1 ∞ be a nondecreasing sequence of positive numbers. We investigate conditions on a class φ(L) under which any function f from this class satisfies estimates of the form S nk(f,x) = o(λ k) a. e., where the right-hand side depends on k only. © 2012 Pleiades Publishing, Ltd.