On the convergence of multiple Walsh-Fourier series of functions of bounded generalized variation (Q1931622)

The convergence of multiple Wash-Fourier series of functions of bounded generalized variation is investigated. Sufficient and necessary conditions on the sequence \(\lambda=\{\lambda_n\}\) are found for the convergence of multiple Walsh-Fourier series of functions of bounded partial \(\lambda\)-variation within the framework of continuous functions. The notation of \(\Lambda\)-variation was introduced by Waterman in 1972. Editorial remark: Theorem 1.1 of this paper and its proof coincide verbatim with Theorem 1.1 of [\textit{U. Goginava} and \textit{A. Sahakian}, Anal. Math. 39, No. 1, 45--56 (2013; Zbl 1299.42017)].