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Isometries of Weighted Bergman Spaces

Published online by Cambridge University Press:  20 November 2018

Clinton J. Kolaski
Clinton J. Kolaski*
Affiliation:
The University of Texas at San Antonio, San Antonio, Texas
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In [2], [8] and [10], Forelli, Rudin and Schneider described the isometries of the Hp spaces over balls and polydiscs. Koranyi and Vagi [6] noted that their methods could be used to describe the isometries of the Hp spaces over bounded symmetric domains. Recently Kolaski [4] observed that the algebraic techniques used above and Rudin's theorem on equimeasurability extended to the Bergman spaces over bounded Runge domains. In this paper we use the same general argument to characterize the onto linear isometries of the weighted Bergman spaces over balls and polydiscs, (all isometries referred to are assumed to be linear).

2. Preliminaries. Horowitz [3] first defined the weighted Bergman space Ap,α(0 < p < ∞, 0 < α < ∞) to be the space of holomorphic functions f in the disc which satisfy

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Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 4 , 01 August 1982 , pp. 910 - 915
Copyright
Copyright © Canadian Mathematical Society 1982

References

References&gt;

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