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Isometries of Bergman Spaces over Bounded Runge Domains

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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1.1. The isometries of the Hardy spaces Hp(0 < p < ∞, p ≠ 2) of the unit disc were determined by Forelli in [2]. Generalizations to several variables: For the polydisc the isometries of Hp onto itself were characterized by Schneider [9]. For the unit ball the case p > 2 was then done by Forelli [3]; Rudin [8] removed the restriction p > 2 by proving a theorem on equimeasurability. Finally, Koranyi and Vagi [6] noted that the methods developed by Forelli, Rudin and Schneider applied to bounded symmetric domains.

In this note it will be shown that their methods also apply to the Bergman spaces over bounded Runge domains. The isometries which are onto are completely characterized; the special cases of the ball and polydisc are particularly nice and are given separately.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 33 , Issue 5 , 01 October 1981 , pp. 1157 - 1164
Copyright
Copyright © Canadian Mathematical Society 1981

References

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