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Projective structures on an annulus and Hankel forms

Published online by Cambridge University Press:  18 May 2009

Jaak Peetre  and
Genkai Zhang
Jaak Peetre
Affiliation:
Matematiska Institutionen, Stockholms Universitet, Box 6701, S-113 85 Stockholm, Sweden
Genkai Zhang
Affiliation:
Matematiska Institutionen, Stockholms Universitet, Box 6701, S-113 85 Stockholm, Sweden
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A general theory of Hankel forms over domains in one or several variables has been set forth in [6]. In [7] the study of Hankel forms over an annulus in the complex plane ℂ was begun. (An extension of the results of [7] to multiply connected domains was given in [4].) The present paper amplifies the results of [7] in various respects. First of all we define and study more general Hankel forms associated with a one parameter family of projective structures on the annulus. This displays several new features. For instance, we are now dealing with quadratic integral metrics which do not correspond to integration of the square of the function with respect to a weight. Furthermore, whereas in [7] essentially only the issue of the boundedness of Hankel forms was studied, we obtain here rather satisfactory Sp-results, even for 0 < p < 1. The question which remains is, of course, to which extent all this extends to multiply connected domains (or more general (open) Riemann surfaces).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 3 , September 1991 , pp. 247 - 266
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

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