Sequences of zeros of analytic function spaces and weighted superposition operators

Abstract

We use properties of the sequences of zeros of certain spaces of analytic functions in the unit disc D to study the question of characterizing the weighted superposition operators which map one of these spaces into another. We also prove that for a large class of Banach spaces of analytic functions in D, Y , we have that if the superposition operator S ϕ associated to the entire function ϕ is a bounded operator from X, a certain Banach space of analytic functions in D, into Y , then the superposition operator S ϕ ′ maps X into Y .2000 Mathematics Subject Classification. Primary 30H30, 30H20; Secondary 46E15, 47H99.

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