Compact Composition Operators between Hardy Spaces

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_j is compact on the Hardy spaces of the open unit ball in .

Keywords: Hardy Spaces, composition operators, boundedness, Compactness, Nevanlinna counting functions.