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Compact Toeplitz operators on weighted harmonic Bergman spaces

Part of: Special classes of linear operators

Published online by Cambridge University Press:  09 April 2009

Karel Stroethoff
Karel Stroethoff
Affiliation:
Department of Mathematical Sciences University of MontanaMissoula, MT 59812-1032USA e-mail: [email protected]
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Abstract

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We consider the Bergman spaces consisting of harmonic functions on the unit ball in Rn that are squareintegrable with respect to radial weights. We will describe compactness for certain classes of Toeplitz operators on these harmonic Bergman spaces.

MSC classification

Secondary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators 47B38: Operators on function spaces (general)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 64 , Issue 1 , February 1998 , pp. 136 - 148
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Axler, S., Bourdon, P., and Ramey, W., Harmonic function theory (Springer, New York, 1992).CrossRefGoogle Scholar
[2]Coifman, R. and Rochberg, R., ‘Representation theorems for holomorphic and harmonic functions,’ Astérisque 77 (1980), 11–66.Google Scholar
[3]Korenblum, B. and Zhu, K., ‘An application of Tauberian theorems to Toeplitz operators,’ J. Operator Theory 33 (1995), 353–361.Google Scholar
[4]Miao, J., ‘Toeplitz operators on harmonic Bergman spaces,’ Integral Equations Operator Theory 27 (1997), 426–438.CrossRefGoogle Scholar
[5]Stroethoff, K., ‘Compact Hankel operators on weighted harmonic Bergman spaces,’ Glasgow Math. J. 39 (1997), 77–84.CrossRefGoogle Scholar
[6]Stroethoff, K., ‘Compact Toeplitz operators on Bergman spaces,’ Math. Proc. Cambridge Phil. Soc., to appear.Google Scholar