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ESSENTIAL NORM OF EXTENDED CESÀRO OPERATORS FROM ONE BERGMAN SPACE TO ANOTHER

Part of: Holomorphic functions of several complex variables

Published online by Cambridge University Press:  12 December 2011

ZHANGJIAN HU
ZHANGJIAN HU*
Affiliation:
Department of Mathematics, Huzhou Teachers College, Huzhou, Zhejiang, 313000, China (email: [email protected])
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Abstract

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Let Ap(φ) be the pth Bergman space consisting of all holomorphic functions f on the unit ball B of ℂn for which , where φ is a given normal weight. Let Tg be the extended Cesàro operator with holomorphic symbol g. The essential norm of Tg as an operator from Ap (φ)to Aq (φ)is denoted by . In this paper it is proved that, for p≤q, with 1/k=(1/p)−(1/q) , where ℜg(z)is the radial derivative of g; and for p>q, with 1/s=(1/q)−(1/p) .

Keywords

Bergman spacesextended Cesàro operatorsessential norm

MSC classification

Secondary: 32A37: Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 85 , Issue 2 , April 2012 , pp. 307 - 314
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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