Geodesic
Isometries of Hp Spaces of Bounded Symmetric Domains
Canadian journal of mathematics, Tome 28 (1976) no. 2, pp. 334-340

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Korányi, Adam; Vági, Stephen. Isometries of Hp Spaces of Bounded Symmetric Domains. Canadian journal of mathematics, Tome 28 (1976) no. 2, pp. 334-340. doi: 10.4153/CJM-1976-035-8
@article{10_4153_CJM_1976_035_8,
     author = {Kor\'anyi, Adam and V\'agi, Stephen},
     title = {Isometries of {Hp} {Spaces} of {Bounded} {Symmetric} {Domains}},
     journal = {Canadian journal of mathematics},
     pages = {334--340},
     year = {1976},
     volume = {28},
     number = {2},
     doi = {10.4153/CJM-1976-035-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1976-035-8/}
}
TY  - JOUR
AU  - Korányi, Adam
AU  - Vági, Stephen
TI  - Isometries of Hp Spaces of Bounded Symmetric Domains
JO  - Canadian journal of mathematics
PY  - 1976
SP  - 334
EP  - 340
VL  - 28
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1976-035-8/
DO  - 10.4153/CJM-1976-035-8
ID  - 10_4153_CJM_1976_035_8
ER  - 
%0 Journal Article
%A Korányi, Adam
%A Vági, Stephen
%T Isometries of Hp Spaces of Bounded Symmetric Domains
%J Canadian journal of mathematics
%D 1976
%P 334-340
%V 28
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1976-035-8/
%R 10.4153/CJM-1976-035-8
%F 10_4153_CJM_1976_035_8

[1] 1. Bochner, S., Classes of holomorphic functions of several variables in circular domains, Proc. Nat. Acad. Sci. 46 (I960), 721–723. Google Scholar

[2] 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] 3. Forelli, F., The isometries of H*, Can. J. Math. 16 (1964), 721–728. Google Scholar

[4] 4. Forelli, F., theorem on isometries and the application of it to the isometries of HP(S) for 2 &lt; p &lt; ∞, Can. J. Math. 25 (1973), 284–289. Google Scholar

[5] 5. Hahn, K. T. and Mitchell, J., Hv spaces on bounded symmetric domains, Trans. Amer. Math. Soc. 146 (1969), 521–531. Google Scholar

[6] 6. Helgason, S., Differential geometry and symmetric spaces, Academic Press, New York, (1962). Google Scholar

[7] 7. Korânyi, A., The Poisson integral for generalized half-planes and bounded symmetric domains, Ann. of Math. 82 (1965), 332–350. Google Scholar

[8] 8. Korânyi, A., and Vagi, S., Inner functions on bounded symmetric domains, to appear. Google Scholar

[9] 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] 10. Moore, C. C., Compactificalion of symmetric spaces II: The Cartan domains, Am. J. Math. 86 (1964), 358–378. Google Scholar

[11] 11. Rudin, W., Function theory in polydiscs (Benjamin, New York, 1969). Google Scholar

[12] 12. Rudin, W., Lp-isometries and equimeasurability, to appear in Indiana J. of Math. Google Scholar

[13] 13. Schneider, R. B., Isometries of Hp(Un), Can. J. Math. 25 (1973), 92–95. Google Scholar

[14] 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

Cité par Sources :