Cesaro summation of Fourier series of functions from multidimensional Waterman classes (Q656302)

The classes \(\Lambda\)BV of functions (of bounded \(\Lambda\)-variation) were defined by \textit{D. Waterman} [Stud. Math. 44, 107--117 (1972; Zbl 0207.06901)] in the one-dimensional case, by \textit{A. A. Saakyan} [Izv. Akad. Nauk Arm. SSR, Mat. 21, No. 6, 517--529 (1986; Zbl 0614.42009)] in the two-dimensional case, and by \textit{A. I. Sablin} [Izv. Vyssh. Uchebn. Zaved., Mat. 1987, No. 10(305), 66--68 (1987; Zbl 0657.42005)] in the case of higher dimensions. In this paper, Cesàro methods of negative order are used to analyse the summability of Fourier series of functions of bounded \(\Lambda\)-variation. The main result proved is a multidimensional analogue of a one-dimensional result by \textit{D. Waterman} in [Stud. Math. 55, 87--95 (1976; Zbl 0332.42009].