Geodesic
Projective structures on an annulus and Hankel forms
Glasgow mathematical journal, Tome 33 (1991) no. 3, pp. 247-266

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

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). 
Peetre, Jaak; Zhang, Genkai. Projective structures on an annulus and Hankel forms. Glasgow mathematical journal, Tome 33 (1991) no. 3, pp. 247-266. doi: 10.1017/S0017089500008314
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[1] 1.Berezin, F. A., General concept of quantization, Commun. Math. Phys. 40 (1975), 153–174. Google Scholar | DOI

[2] 2.Gunning, R. G., Lectures on Riemann surfaces (Princeton University Press, 1966). Google Scholar

[3] 3.Gustafsson, B. and Peetre, J., Notes on projective structures on complex manifolds, Nagoya Math. J. 116 (1989), 63–88. Google Scholar | DOI

[4] 4.Gustafsson, B. and Peetre, J., Hankel forms on multiply connected domains. Part Two. The case of higher connectivity, Complex Variables 13 (1990), 239–250. Google Scholar

[5] 5.Janson, S., Hankel operators between weighted Bergman spaces, Ark. Mat. 26 (1988), 205–219. Google Scholar | DOI

[6] 6.Janson, S., Peetre, J. and Rochberg, R., Hankel forms and the Fock space, Revista Mat. Iberoamericana. 3 (1987), 61–138. Google Scholar | DOI

[7] 7.Peetre, J., Hankel forms on multiply connected domains. Part One. The case of connectivity two, Complex Variables 10 (1988), 123–139. Google Scholar

[8] 8.Peetre, J., The Berezin transform and Ha-plitz operators, J. Operator Theory 24 (1990), 165–186. Google Scholar

[9] 9.Peetre, J., New Thoughts on Besov spaces (Duke University Mathematics Series 1), Duke University, Durham, 1976. Google Scholar

[10] 10.Peetre, J. and Karlsson, J., Rational approximation—analysis of the work of Pekarskil, Rocky Mountain J. Math. 19 (1989), 313–333. Google Scholar | DOI

[11] 11.Rochberg, R., Decomposition theorems for Bergman spaces and applications, in: Operators and Function Theory (ed. Power, S. C.), Proceedings, Lancaster 1984, p. 225–277. Reidel, Dordrecht, 1985. Google Scholar

[12] 12.Rochberg, R. and Semmes, S., A decomposition theorem for functions in BMO and application, j. Functional Analysis 67 (1986), 228–263. Google Scholar | DOI

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