PRODUCTS OF RADIAL DERIVATIVE AND WEIGHTED COMPOSITION OPERATORS FROM WEIGHTED BERGMAN-ORLICZ SPACES TO WEIGHTED-TYPE SPACES

Let H(B-n) be the space of all holomorphic functions on the unit ball B-n of C-n, phi a holomorphic self-map of B-n, u is an element of H(B-n), and R the radial derivative operator on H(B-n). Two operators on H(B-n) are defined by RWu,phi f(z) = R (u(z) f(phi(z))) and W-u,W-phi Rf(z) = u(z)Rf(phi(z)), which are called the products of radial derivative operators and weighted composition operators. In this paper, the boundedness and compactness of the operators RWu,phi and Wu,phi R from weighted Bergman-Orlicz spaces to a class of weighted-type spaces are characterized.