  The purpose of this paper is to prove that if a pseudoconvex domains
$\Omega\subset\mathbb{C}^n$ satisfies Bell-Ligocka's Condition R and admits a
``good" dilation, then the Bergman projection has local $L^p$-Sobolev and
H\"older estimates. The good dilation structure is phrased in terms of uniform
$L^2$ pseudolocal estimates for the Bergman projection on a family of
anisotropic scalings. We conclude the paper by showing that $h$-extendible
domains satisfy our hypotheses.
