Integral of multiplication of two $\iint Q(f(r,\theta ))Q(h(r,\theta )) \,dr\,d\theta $ function?

Question

I have an integral,

\begin{align} y & = \int_0^\infty \int_0^{2\pi} Q\left( - (r\cos \theta + b)a \right) Q\left( { - (r\sin \theta + c)d} \right)f\left( {r,\theta } \right) \, dr \, d\theta \\[6pt] & = \int_0^\infty g(r)f(r)\,dr \end{align}

where, $z = r{e^{j\theta }};z \in C$ and $a,b,c,d \in R$.

I wanted to find ${g(r )}$.

1. Is there any way I can find that?
2. Is there any theorem that might help me find that?