The Essential Norm of a Composition Operator on a Planar Domain

By Stephen D. Fisher and Jonathan E. Shapiro

This paper appears in the Illinois Journal of Mathematics, 43 (1999), 113-130.


We generalize to finitely connected planar domains the result of Joel Shapiro which gives a formula for the essential norm of a composition operator. In the process, we define and give some properties of a generalization of the Nevanlinna counting function and prove generalizations of the Littlewood inequality, the Littlewood-Paley identity, and change of variable formulas, as well.

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