On the Borel Summability of Double Fourier Series

Let f(u, v) be a function integrable in the sense of Lebesgue over the square (0, 2π; 0, 2π) and periodic with period 2π in each variable. Let
∅(u,v)=1/4{f(x+u,y+v)+f(x-u,y+v)+f(x+u,y-v)+f(x-u,y-v)-4}.