Multiple Fourier coefficients and generalized Lipschitz classes in uniform metric

In this study, we give the necessary and sufficient conditions for a function f(x,y)=∑j,k∈Zcjkexp⁡(ijx+iky)f(x,y)=∑j,k∈Zcjkexp⁡(ijx+iky) to belong to the generalized Lipschitz classes Hω,m,nHω,m,n and hω,m,nhω,m,n in the uniform metric defined by the mixed difference of orders m,n∈Nm,n∈N in terms of {cjk}j,k∈Z{cjk}j,k∈Z.