Essential norms of composition operators. (English) Zbl 1065.47027

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.


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