By Stephen D. Fisher and Jonathan E. Shapiro
This paper appears in the Illinois Journal of Mathematics, 43 (1999),
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,
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