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

Abstract

Abstract Let φ be an analytic self-map of the open unit disk 𝔻 in the complex plane ℂ and u be an analytic function on 𝔻. The weighted composition operator is defined on the space H(𝔻) of analytic functions on 𝔻 by u C φ f = u ⋅ ( f ∘ φ ) , f ∈ H ( D ) . $$u{C_\varphi }f = u \cdot \left( {f \circ \varphi } \right),\quad f \in H\left(D\right).$$ The boundedness and the compactness of weighted composition operators from the Besov space into nth weighted type spaces are given in this work.