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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  and
Horacio Porta
Earl Berkson
Affiliation:
Department of Mathematics, University of Illinois, Urbana, Illinois 61801
Horacio Porta
Affiliation:
Department of Mathematics, University of Illinois, Urbana, Illinois 61801
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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
Information
Glasgow Mathematical Journal , Volume 21 , Issue 2 , July 1980 , pp. 199 - 204
Copyright
Copyright © Glasgow Mathematical Journal Trust 1980

References

REFERENCES

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