  Using the logarithmic capacity, we give quantitative estimates of the Green
function, as well as lower bounds of the Bergman kernel for bounded
pseudoconvex domains in $\mathbb C^n$ and the Bergman distance for bounded
planar domains. In particular, it is shown that the Bergman kernel satisfies
$K_\Omega(z)\gtrsim \delta_\Omega(z)^{-2}$ for any bounded pseudoconvex domain
with $C^0-$boundary. An application to holomorphic motions is given.
