On the convergence of double Fourier series of functions of bounded   partial generalized variation
  The convergence of double Fourier series of functions of bounded partial $\Lambda$-variation is investigated. The sufficient and necessary conditions on the sequence $\Lambda=\{\lambda_n\}$ are found for the convergence of Fourier series of functions of bounded partial $\Lambda$-variation. 
Ushangi Goginava and Artur Sahakian
math.AP