  We will find Green's function for the standard weighted Laplacian and use the
corresponding Green's potential to solve Poisson's equation in the unit disc
with zero boundary values, in the sense of radial $L^1$-means, for complex
Borel measures $\mu$ satisfying the condition $\int_\mathbb{D}
(1-|w|^2)^{\alpha+1} d|\mu|(w) < \infty$ for $\alpha>-1$.
