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Isometries of Hp Spaces of Bounded Symmetric Domains

Published online by Cambridge University Press:  20 November 2018

Adam Korányi  and
Stephen Vági
Adam Korányi
Affiliation:
Yeshiva University, New York, N. Y.
Stephen Vági
Affiliation:
DePaul University, Chicago, Illinois
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The isometries of the Hardy spaces Hv (0 < p < ∞, p ≠ 2) of the unit disc were determined by Forelli in 1964 [3]. For p = 1 the result had been found earlier by deLeeuw, Rudin and Wermer [2]. For several variables the state of affairs at present is this: For the polydisc the isometries of Hp onto itself have been characterized by Schneider [13]. For the unit ball the same result was proved in the case p > 2 by Forelli [4]. Finally in [12] Rudin removed the restriction p > 2 and also established some results about isometries of Hp of the ball and the polydisc into itself.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 2 , 01 April 1976 , pp. 334 - 340
Copyright
Copyright © Canadian Mathematical Society 1976

References

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