Essential norms of composition operators between Hardy spaces of the unit disc

Luo Luo , Kai Li

Chinese Annals of Mathematics, Series B ›› 2011, Vol. 32 ›› Issue (2) : 209 -214.

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Chinese Annals of Mathematics, Series B ›› 2011, Vol. 32 ›› Issue (2) : 209 -214. DOI: 10.1007/s11401-011-0637-4
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Essential norms of composition operators between Hardy spaces of the unit disc

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Abstract

The authors express the essential norms of composition operators between Hardy spaces of the unit disc in terms of the natural Nevanlinna counting function.

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Essential norm / Composition operators / Hardy spaces

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Luo Luo, Kai Li. Essential norms of composition operators between Hardy spaces of the unit disc. Chinese Annals of Mathematics, Series B, 2011, 32(2): 209-214 DOI:10.1007/s11401-011-0637-4

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Luo L.. The essential norm of a composition operator on the Bergman space of the unit ball. Complex Variables, 2004, 49: 845-850

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Luo L.. The essential norm of a composition operator on Hardy space of the unit ball (in Chinese). Chin. Ann. Math., 2007, 28A(6): 805-810

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Shapiro J. H.. The Essential Norm of a composition operator. Ann. of Math., 1987, 125: 375-404

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Smith W.. Composition operators between Bergman and Hardy spaces. Trans. Amer. Math. Soc., 1996, 348: 2331-2347

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Zhu K.. Duality of Bloch spaces and norm convergence of Taylor series. Michigan Math. J., 1991, 38: 89-101

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Zhu K. H.. Operator Theory in Function Space, 1990, New York: Marcel-Dekker

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