(untitled) (Analysis in Theory and Applications, 2025)
For complex-valued functions f L^1(R^2_+), where R_+ := [0,∞) we give sufficient conditions under which the double cosine or cosine-sine Fourier transform of f belongs to a generalized Lipschitz class defined by the mixed modulus of smoothness of orders m,n N = {1,2,… } in uniform metric. The sharpness of these conditions is established under some restriction for non-negative functions.