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ESSENTIAL NORM OF EXTENDED CESÀRO OPERATORS FROM ONE BERGMAN SPACE TO ANOTHER
Published online by Cambridge University Press: 12 December 2011
Abstract
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) .
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- Research Article
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- Copyright © Australian Mathematical Publishing Association Inc. 2011
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