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Toeplitz and Hankel type operators on an annulus

Part of: Special classes of linear operators

Published online by Cambridge University Press:  26 February 2010

Qingtang Jiang  and
Lizhong Peng
Qingtang Jiang
Affiliation:
Institute of Mathematics, Peking University, Beijing 100871, People's Republic of China.
Lizhong Peng
Affiliation:
Institute of Mathematics, Peking University, Beijing 100871, People's Republic of China.
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Extract

Let Ω be a regular domain in the extended complex plane, i.e., it is a bounded domain and its boundary consists of a finite number of disjoint analytic simple closed curves. Let dm(z) be the Lebesgue area measure on Ω and let ds = dm(z)/ω(z) be the Poincare metric on Ω, a Riemannian metric of negative constant curvature. It may be proved that Ω(z) ≈ Euclidean distance from z to the boundary of Ω (see [8]).

MSC classification

Secondary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators
Type
Research Article
Information
Mathematika , Volume 41 , Issue 2 , December 1994 , pp. 266 - 276
Copyright
Copyright © University College London 1994

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References

1.Arazy, J., Fisher, S. and Peetre, J.. Hankel operators in Bergman spaces. Amer. J. Math., 110 (1988), 989–1053.CrossRefGoogle Scholar
2.Arazy, J., Fisher, S. and Peetre, J.. Hankel operators on planar domains. Constructive Approximation, 6 (1990), 113–138.CrossRefGoogle Scholar
3.Axler, S.. The Bergman kernel, the Bloch space, and commutators of multiplication operators. Duke Math. J., 53 (1986), 315–332.CrossRefGoogle Scholar
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.Janson, S.. Hankel operators between weighted Bergman spaces. Ark. Math., 26 (1988), 205–219.CrossRefGoogle Scholar
6.Janson, S. and Peetre, J.. Paracommutators-boundedness and Schatten-von Neumann properties. Trans. Amer. Math. Soc., 305 (1988), 467–504.Google Scholar
7.Janson, S., Peetre, J. and Rochberg, R.. Hankel forms and the Fock space. Rev. Mat. Ibero-Amer., 3 (1987), 61–138.CrossRefGoogle Scholar
8.Peetre, J.. Hankel forms on multiply connected plane domains. Complex Variables, 10 (1988), 123–139.Google Scholar
9.Peetre, J. and Zhang, G.. Projective structures on an annulus and Hankel forms. Glasgow Math. J., 33 (1991), 247–266.CrossRefGoogle Scholar
10.Peller, V. V.. Hankel operators of class γp and applications. Math. UssR. Sborrik, 41 (1982), 443–479.CrossRefGoogle Scholar
11.Peng, L.. Paracommutator of Schatten-von Neumann class Sp, O<P<1. Math. Scand., 61 (1987), 68–92.Google Scholar
12.Peng, L.. Toeplitz-Hankel type operators on Bergman space. Mathematika, 40 (1993), 345–356.CrossRefGoogle Scholar
13.Peng, L., Rochberg, R. and Wu, Z.. Laguerre polynomials and Hankel operators on Bergman space. Studia Math., 102 (1992), 57–75.Google Scholar
14.Peng, L. and Xu, C.. Jacobi polynomial and Toeplitz-Hankel type operators. Complex Variables, 22 (1993), 1–25.Google Scholar
15.Peng, L. and Zhang, G.. Middle Hankel operators on Bergman space. In Function Spaces, edited by Jarosz, K., Lecture Notes in Pure and Applied Math., Series 136 (Marcel Dekker, 1991), 225–236.Google Scholar
16.Szegö, G., Orthogonal Polynomials. Amer. Math. Soc. Colloq. Publications, 23 (1939).Google Scholar