I was wondering if anyone could provide me with the proof of the pointwise convergence theorem on double fourier series. Namely:

Let f be a continuous function on <-pi,pi>^2 with bounded partial derivatives fx and fy. Then:
a) if there is a neighbourhood of the interior point (x,y) in which the second partial derivative fxy exists, then the fourier serie of f converges to f(x,y)
b) if f is double periodic and has continuous derivatives fx, fy, and fxy then the fourier serie convrges to f everywhere.