Essential norms of weighted composition operators between Bloch-type spaces. (English) Zbl 1061.30023

MacCluer, Barbara D.; Zhao, Ruhan

Rocky Mt. J. Math. 33, No. 4, 1437-1458 (2003).

For \(\alpha>0\) let \(B_\alpha\) denote the space of analytic functions \(f\) in the unit disk \(D\) such that \(\sup_{x\in D}(1-|z|^2)^\alpha |f'(z)|<\infty\). For an analytic function \(u\) in \(D\) and an analytic selfmap \(\varphi\) of \(D\) the paper studies the weighted composition operator \(C\) defined on \(B_\alpha\) as follows: \(Cf=u f(\varphi)\), \(f\in B_\alpha\). The main result of the paper is a formula for the essential norm of \(C\) on \(B_\alpha\).

Reviewer: Kehe Zhu (Albany)

MSC:

30D45	Normal functions of one complex variable, normal families
47B33	Linear composition operators

Keywords:

Lipschitz space; Bloch space