Essential norms of composition operators. (English) Zbl 1065.47027

Gorkin, Pamela; MacCluer, Barbara D.

Integral Equations Oper. Theory 48, No. 1, 27-40 (2004).

Recently, there has been considerable interest in studying lower and upper estimates for the essential norms of composition operators in function spaces. Sometimes, as a consequence, a necessary and sufficient condition for the composition operator to be compact on the function space can be obtained. In this paper, the authors estimate the essential norm of a composition operator acting from Hardy space \(H^p\) to \(H^q\) in one or several variables, where \(p>q\). When \(p=\infty\) and \(q=2\), they also give an exact formula for the essential norm.

Reviewer: Zehua Zhou (Tianjin)

MSC:

47B33	Linear composition operators
47B38	Linear operators on function spaces (general)
47A30	Norms (inequalities, more than one norm, etc.) of linear operators

Keywords:

composition operator; essential norm; Hardy space