Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-22T20:36:22.641Z Has data issue: false hasContentIssue false

The group of isometries on Hardy spaces of the n-ball and the polydisc

Published online by Cambridge University Press:  18 May 2009

Earl Berkson
Affiliation:
Department of Mathematics, University of Illinois, Urbana, Illinois 61801
Horacio Porta
Affiliation:
Department of Mathematics, University of Illinois, Urbana, Illinois 61801
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let C be the complex plane, and U the disc |Z| < 1 in C. Cn denotes complex n-dimensional Euclidean space, <, > the inner product, and | · | the Euclidean norm in Cn;. Bn will be the open unit ball {z ∈ Cn:|z| < 1}, and Un will be the unit polydisc in Cn. For l ≤ p < ∞, p ≠ 2, Gp(Bn) (resp., Gp(Un)) will denote the group of all isometries of Hp(Bn) (resp., Hp(Un)) onto itself, where Hp(Bn) and HP(Un) are the usual Hardy spaces.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1980

References

REFERENCES

1.Berkson, E. and Porta, H., The group of isometries of H p;, Ann. Mat. Pura Appl., (IV), CXIX, (1979), 231238.CrossRefGoogle Scholar
2.Berkson, E. and Porta, H., The p-norms of peak functions, Proceedings of (Summer,1978) Special Session on Operator Theory and Functional Analysis, Research Notes in Math., No. 38 (Pitman, 1979), 115121.Google Scholar
3.Koranyi, A. and Vagi, S., Isometries of H p spaces of bounded symmetric domains, Canad. J. Math., 28 (1976), 334340.CrossRefGoogle Scholar
4.Schwartz, H., Composition operators in Hp, Thesis, (University of Toledo, 1969).Google Scholar
5.Zygmund, A., Trigonometric Series (2nd edition), Vol. 2, (Cambridge University Press, 1959).Google Scholar