I want to do a 3-dimensional Fourier series expansion on this function$$\frac{\cos (x) \cos (y) \cos (z)-\sin (x) \sin (y) \sin (z)}{\left[(a+\sin (y)+\cos (z))^2+(b+\cos (x)+\sin (z))^2+(c+\sin (x)+\cos (y))^2\right]^{\frac{3}{2}}}$$ when $a,b,c\in(0,2)$, for which the denominator is possible to vanish at some points.
Is it really square-integrable on $[0,2\pi]\times[0,2\pi]\times[0,2\pi]$? Is the Fourier series expansion well-defined here?
Thanks in advance!