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Compact Composition Operators between Hardy Spaces

Elhadi Elnour Elniel

Abstract

We characterise composition operators between Hardy 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 Hardy spaces of the open unit ball in n C .

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Key concepts: Hardy space, Mathematics, Compact space, Composition (language), Bounded function, Composition operator, Pure mathematics, Unit sphere