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Toeplitz operators on harmonic Bergman spaces

Published online by Cambridge University Press:  22 January 2016

Boo Rim Choe ,
Young Joo Lee  and
Kyunguk Na
Boo Rim Choe
Affiliation:
Department of Mathematics, Korea University, Seoul 136-701, Korea, cbr@korea.ac.kr
Young Joo Lee
Affiliation:
Department of Mathematics, Mokpo National University, Chonnam 534-729, Korea, yjlee@mokpo.ac.kr
Kyunguk Na
Affiliation:
Department of Mathematics, Korea University, Seoul 136-701, Korea, nakyunguk@korea.ac.kr
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Abstract

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We study Toeplitz operators on the harmonic Bergman spaces on bounded smooth domains. Two classes of symbols are considered; one is the class of positive symbols and the other is the class of uniformly continuous symbols. For positive symbols, boundedness, compactness, and membership in the Schatten classes are characterized. For uniformly continuous symbols, the essential spectra are described.

Keywords

47B3531B05
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 174 , 2004 , pp. 165 - 186
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2004

References

[1] Axler, S., Bourdon, P. and Ramey, W., Harmonic function theory, Springer-Verlag, New York, 1992.CrossRefGoogle Scholar
[2] Choe, B. R., Koo, H. and Yi, H., Positive Toeplitz operators between the harmonic Bergman spaces, Potential Analysis, 17 (2002), 307–335.Google Scholar
[3] Dunford, N. and Schwartz, J. T., Linear operators, Part I, Interscience Publishers, Inc., New York, 1958.Google Scholar
[4] Jovović, M., Compact Hankel operators on the harmonic Bergman spaces, Integr. Eqn. Oper. Theory, 22 (1995), 295–304.Google Scholar
[5] Kang, H. and Koo, H., Estimates of the harmonic Bergman kernel on smooth domains, J. Funct. Anal., 185 (2001), 220–239.Google Scholar
[6] Miao, J., Toeplitz operators on harmonic Bergman spaces, Integr. Eqn. Oper. Theory, 27 (1997), 426–438.CrossRefGoogle Scholar
[7] Oleinik, O. L., Embedding theorems for weighted classed of harmonic and analytic functions, J. Soviet Math., 9 (1978), 228–243.Google Scholar
[8] Stroethoff, K., Compact Toeplitz operators on weighted harmonic Bergman spaces, J. Austral. Math. Soc. (Series A), 64 (1998), 136–148.CrossRefGoogle Scholar
[9] Zhu, K., Operator theory in function spaces, Marcel Dekker. New York and Basel, 1989.Google Scholar
[10] Zhu, K., Positive Toeplitz operators on weighted Bergman spaces of bounded symmetric domains, Operator Th., 20 (1988), 329–357.Google Scholar