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2014•Unpublished venueRequires access

On the theory and applications of Hardy and Bergman spaces

ElhadiElnourElnieland M. E. Hassan

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Abstract

We study composition operators between higher orders weighted Bergman spaces. Certain growth conditions for generalized Nevanlinna counting functions of the inducing map are shown to be necessary and sufficient for such operators to be bounded or compact. Under a mind condition we show that a composition operators C is compact on the higher order weighted Bergman spaces and Hardy spaces of the open unit ball in nC if and only if 0 as |z | 1-.

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What this paper is about

We study composition operators between higher orders weighted Bergman spaces. Certain growth conditions for generalized Nevanlinna counting functions of the inducing map are shown to be necessary and sufficient for such operators to be bounded or compact. Under a mind condition we show that a composition operators C is compact on the higher order weighted Bergman spaces and Hardy spaces of the open unit ball in nC if and only if 0 as |z | 1-.

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Available abstract

We study composition operators between higher orders weighted Bergman spaces. Certain growth conditions for generalized Nevanlinna counting functions of the inducing map are shown to be necessary and sufficient for such operators to be bounded or compact. Under a mind condition we show that a composition operators C is compact on the higher order weighted Bergman spaces and Hardy spaces of the open unit ball in nC if and only if 0 as |z | 1-.

Key concepts: Mathematics, Hardy space, Compact space, Pure mathematics, Bounded function, Bergman space, Unit sphere, Operator theory

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