Integration over annulus with infinite outer radius as an integral over a half-space

Question

If I have an integral over an infinite annulus $\mathcal{A} = \{(x, y)~|~x^{2} + y^{2} \geq R \}$, is there a way to transform the variable of integration/coordinates so that the integral is over a half-space? In the case of rotationally symmetric integrand, $\int_{R}^{\infty}\int_{0}^{2\pi}d\rho d\phi\rho f(\rho)$ becomes some integral over $x,y$ which is now rectangular?