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

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 B p ( 1 ≤ p < ∞ ) into the weighted-type space H μ ∞ consisting of the analytic functions on D such that sup z ∈ D μ ( 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 B p into H μ ∞ , 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 B p and B M O A into the α -Bloch spaces.