Approximation in weighted Bergman spaces and Hankel operators on strongly pseudoconvex domains

Suppose D is a bounded strongly pseudoconvex domain in $${{\mathbb {C}}}^n$$ with smooth boundary, and let $$\rho $$ be its defining function. For $$1< p-1$$ , we show that the weighted Bergman projection $$P_\alpha $$ is bounded on $$L^p(D, |\rho |^\alpha dV)$$ . With non-isotropic estimates for $$\overline{\partial }$$ and Stein’s theorem on non-tangential maximal operators, we prove that bounded holomorphic functions are dense in the weighted Bergman space $$A^p(D, |\rho |^\alpha dV)$$ , and hence Hankel operators can be well defined on these spaces. For all $$1