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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

1. Bochner, S., Classes of holomorphic functions of several variables in circular domains, Proc. Nat. Acad. Sci. 46 (I960), 721–723.Google Scholar
2. deLeeuw, K., Rudin, W., and Wermer, J., The isometries of some function spaces, Proc. Amer. Math. Soc. 11 (1960), 694–698.Google Scholar
3. Forelli, F., The isometries of H*, Can. J. Math. 16 (1964), 721–728.Google Scholar
4. Forelli, F., theorem on isometries and the application of it to the isometries of HP(S) for 2 < p < ∞, Can. J. Math. 25 (1973), 284–289.Google Scholar
5. Hahn, K. T. and Mitchell, J., Hv spaces on bounded symmetric domains, Trans. Amer. Math. Soc. 146 (1969), 521–531.Google Scholar
6. Helgason, S., Differential geometry and symmetric spaces, Academic Press, New York, (1962).Google Scholar
7. Korânyi, A., The Poisson integral for generalized half-planes and bounded symmetric domains, Ann. of Math. 82 (1965), 332–350.Google Scholar
8. Korânyi, A., and Vagi, S., Inner functions on bounded symmetric domains, to appear.Google Scholar
9. Korânyi, A. and Wolf, J. A., Realization of Hermitian symmetric spaces as generalized halfplanes, Ann. of Math. 81 (1965), 265–288.Google Scholar
10. Moore, C. C., Compactificalion of symmetric spaces II: The Cartan domains, Am. J. Math. 86 (1964), 358–378.Google Scholar
11. Rudin, W., Function theory in polydiscs (Benjamin, New York, 1969).Google Scholar
12. Rudin, W., Lp-isometries and equimeasurability, to appear in Indiana J. of Math.Google Scholar
13. Schneider, R. B., Isometries of Hp(Un), Can. J. Math. 25 (1973), 92–95.Google Scholar
14. Stoll, M., Harmonic majorants for plurisubharmonic functions on bounded symmetric domains with applications to the spaces H$ and N*, to appear in J. Reine Angew. Math.Google Scholar