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

Suppose D is a bounded strongly pseudoconvex domain in C-n with smooth boundary, and let rho be its defining function. For 1 < p < infinity and alpha > -1, we show that the weighted Bergman projection P-alpha is bounded on L-P (D, vertical bar rho vertical bar(alpha) dV). With non-isotropic estimates for (partial derivative) over bar 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, vertical bar rho vertical bar(alpha) dV), and hence Hankel operators can be well defined on these spaces. For all 1 < p, q < infinity we characterize bounded (resp. compact) Hankel operators from p-th weighted Bergman space to q-th weighted Lebesgue space with possibly different weights. As a consequence, we generalize the main results in Pau et al. (Indiana Univ Math J 65:1639-1673, 2016) and resolve a question posed in Lv and Zhu (Integr Equ Oper Theory, 2019).