Essential norm of weighted composition operator between α-Bloch space and β-Bloch space in polydiscs

Abstract

Let φ(z)=(φ1(z),…,φn(z)) be a holomorphic self-map of &#x1D53B;n and ψ(z) a holomorphic function on &#x1D53B;n, where &#x1D53B;n is the unit polydiscs of ℂn. Let 0<α, β<1, we compute the essential norm of a weighted composition operator ψCφ between α-Bloch space ℬα(&#x1D53B;n) and β-Bloch space ℬβ(&#x1D53B;n).