Weighted norm inequalities for derivatives on Bergman spaces

An equivalent norm in the weighted Bergman space A ω p , induced by an ω in a certain large class of non-radial weights, is established in terms of higher order derivatives. Other Littlewood–Paley inequalities are also considered. On the way to the proofs, we characterize the q-Carleson measures for the weighted Bergman space A ω p and the boundedness of a Hörmander-type maximal function. Results obtained are further applied to describe the resolvent set of the integral operators T g (f)(z)=∫ 0 z g ′ (ζ)f(ζ)dζ acting on A ω p .