Weighted composition operators from the Besov spaces into the weighted-type space [formula omitted

Abstract

Let μ denote a positive continuous function on the open unit disk D. In this work, we characterize the bounded weighted composition operators from the analytic Besov spaces Bp (1≤p<∞) into the weighted-type space Hμ∞ consisting of the analytic functions on D such that supz∈Dμ(z)|f(z)|<∞ and determine their operator norms. We also determine the essential norm of the bounded weighted composition operators acting on the Dirichlet space and obtain explicit estimates when p=1. In the general case when the operator maps Bp into Hμ∞, we derive an approximation of the essential norm that yields a characterization of the compact weighted composition operators. Finally, we derive characterizations of the bounded and the compact weighted composition operators from the spaces of antiderivatives of functions in Bp and BMOA into the α-Bloch spaces.