On the norm of a composition operator with linear fractional symbol. (English) Zbl 1071.47508

Hammond, Christopher

Acta Sci. Math. 69, No. 3-4, 813-829 (2003).

Given an analytic map \(\varphi: \mathbb D \to \mathbb D\), the composition operator on the \(p\)-th Hardy space \(C_\varphi: \mathbb H^p \to \mathbb H^p\) is given by \(C_\varphi (f):= f \circ \varphi\) \(\forall \;f \in \mathbb H ^p\). This paper deals with the computation of the norm of \(C_\varphi\) and other related questions in the case of \(\varphi\) linear fractional maps. The paper contains background information and is very agreeable to read.

Reviewer: Luigi de Pascale (Pisa)

MSC:

47B33	Linear composition operators
47A30	Norms (inequalities, more than one norm, etc.) of linear operators
30D55	\(H^p\)-classes (MSC2000)

Keywords:

composition operator; Hardy spaces