Some Problems On The Convergence And Divergence Of Multiple Fourier Series

In mathematics,the theory of Fourier series is mainly about the question of whether the Fourier series of a periodic function converges to the given function.Convergence is not necessarily given in the general case,and certain criteria must be met for convergence to occur.The function of bounded generalized variation as a important class,the Fourier series of which is convergence or not,as well as the condition of convergence are primarily concerned.In this paper,we present the Abel sum of n-variable function's Fourier series and the solution of Dirichlet question on the polydisk,in addition,we summarize the convergence of functions of bounded partial generalized variation,and we extend one-variable functions of bounded partial ?-variation to n-variable function of bounded partial ?-variation.