Summability of multiple Fourier series of functions of bounded generalized variation (Q2446177)

Let \(d \geq 1\), \(f\) a function defined on \(R^d\) having period \(2\pi\) in each variable, \(T=[0,2\pi]\) and \(H _j = \{ h_{nj} \}\), \(( j=1,2,\dots ,d, n=1 ,2,\dots d)\) sequences of positive numbers. The paper studies the problem of the convergence of the rectangular partial sums of Fourier series of functions f of bounded \(( H_1, H_2, \dots, H_d )\) - variation on \(T^d\) and gives necessary and sufficient conditions for the convergence of the Cesàro means of Fourier series of these functions \(f\).