WEIGHTED NORM INEQUALITIES FOR DERIVATIVES ON BERGMAN SPACES

An equivalent norm in the weighted Bergman space A p omega , induced by an omega 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 p omega and the boundedness of a H & ouml;rmander-type maximal function. Results obtained are further applied to describe the resolvent set of the integral operators T g (f)(z) = f 0 z g ' (()f (() c1( acting on A p omega .