On the convergence of multiple Fourier series of functions of bounded partial generalized variation

The convergence of multiple Fourier series of functions of bounded partial $% \Lambda$-variation is investigated. The sufficient and necessary conditions on the sequence $\mathrm{\Lambda }=\{{\lambda }_n\}$ are found for the convergence of multiple Fourier series of functions of bounded partial $\mathrm{\Lambda }$-variation.