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Toeplitz Operators with BMO Symbols of Several Complex Variables

Toeplitz Operators with BMO Symbols of Several Complex Variables
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摘要 In this note we prove that the boundedness and compactness of the Toeplitz operator on the Bergman space L2a （Bn） for several complex variables with a BMO1 symbol is completely determined by the boundary behavior of its Berezin transform. In this note we prove that the boundedness and compactness of the Toeplitz operator on the Bergman space L2a （Bn） for several complex variables with a BMO1 symbol is completely determined by the boundary behavior of its Berezin transform.
作者 Zhong Hua HE Guang Fu CAO
机构地区 School of Mathematics and Information Sciences
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第3期599-608,共10页 数学学报（英文版）
基金 Supported by National Natural Science Foundation of China (Grant No. 10971040) Research Foundation for Doctorial Program of Higher Education
关键词 Toeplitz operator Bergman space Berezin transform Toeplitz operator, Bergman space, Berezin transform
分类号 O177 [理学—基础数学]
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参考文献9

  • 1Axler, S., Zheng, D.: Compact operator via the Berezin transform. Indiana Univ. Math. J., 47(2), 387-400 (1998).
  • 2Bekoue, D., Berger, C. A., Cobarn, L. A., et al.: BMO in the Bergman metric on bounded symmetric domains. J. Funct. Anal., 93(2), 310-350 (1990).
  • 3Stroethoff, K., Zheng, D. C.: Toeplitz and Hankel operators on Bergman spaces. Trans. Amer. Math. Soc., 329(2), 773-794 (1992).
  • 4Zhu, K. H.: Positive Toeplitz operators on weighted Bergman spaces of bounded symmetric domains. J. Operator Theory, 20(2), 329-357 (1998).
  • 5Zorboska, N.: The Berezin transform and radial operators. Proc. Amer. Math. Soc., 131(3), 793-800 (2003).
  • 6Hedenmalm, H., Korenblum, B., Zhu, K.: Theory of Bergman Spaces, Graduate Texts in Mathematics, Vol. 199, Springer-Verlag, New York, 2000.
  • 7Zhu, K. H.: Operator theory in function spaces. In: A Series of Monographs and Textbooks in Pure Appl. Math., Vol. 139, Marcal Dekker, Inc, New York, 1990.
  • 8Zorboska, N.: Toeplitz operator with BMO symbols and the Berezin transform. Int. J. Math. Sci., 46, 2929-2945 (2003).
  • 9Luecking, D. H.: Trace ideal oriteria for Toeplitz operators. J. Funct. Anal., 73(2), 345-368 (1987).
Acta Mathematica Sinica,English Series
2012年 第3期

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