Products of composition, multiplication and radial derivative operators between Banach spaces of holomorphic functions on the unit ball

Abstract

ABSTRACT Let denote the space of holomorphic functions on the unit ball of , , , . Let , and denote the composition, multiplication and radial derivative operators, respectively. To treat the operators induced by products of these operators in a unified manner, we study the operator . We characterize the boundedness, compactness and order boundedness of mapping from a large class of Banach spaces X of holomorphic functions into the weighted-type space (or ), and give its norm estimate and essential norm estimate. We also obtain the above characterizations and estimates for the weighted composition operator mapping from X into the Bloch-type space (or ). Our results show that the above characterizations and estimates of these operators depend only on the symbols and the norm of the point-evaluation functionals on the domain space.