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

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.

### 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