讨论了单位球的加权Bergman空间Aαp(Bn,dVα)(1<p<∞)上具有L1(Bn)符号的Toeplitz算子,利用单位球上Toeplitz算子的Berezin变换,等价刻画了Aαp(Bn,dVα)上具有L1(Bn)符号的Toeplitz算子的有界性和紧性,推广了Agbor对La2(D,dA)上具有L1(D)符号的Toeplitz算子的有界性和紧性等价刻画的结论.
Abstract
We investigate the boundedness and compactness of Toeplitz operators with L1 symbols on weighted Bergman spaces of the unit ball Aαp(Bn, dVα) (1<p<∞). We describe the boundedness and compactness of Toeplitz operators with L1 symbols on Aαp(Bn, dVα) equivalently by using the Berezin transform of the Toeplitz operators, and promote the conclusion given by Agbor about the boundedness and compactness of Toeplitz operators with L1 symbols on Bergman space of the unit disk La2(D).
关键词
加权Bergman空间 /
Toeplitz算子 /
Berezin变换
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Key words
weighted Bergman space /
Toeplitz operator /
Berezin transform
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参考文献
[1] Zhu K. H., Spaces of Holomorphic Functions in the Unit Ball, Springer Science+Business Media, New York, 2005.
[2] Raimondo R., Toeplitz operators on the Bergman spaces of the unit ball, Bull. Austral. Math. Soc., 2000, 62(2): 273-285.
[3] Zhu K. H., Positive Toeplitz operators on weighted Bergman spaces of bounded symmetric domains, J. Oper. Th., 1988, 20(2): 329-357.
[4] Zorboska N., Toeplitz operator with BMO symbols and the Berezin transform, IJMMS, 2003, 2003(46): 2929-2945.
[5] Agbor D., Boundness and Compactness of Toeplitz Operator with L1 Symbols on the Bergman Space, Dept. of Mathematics, Faculty of Science, University of Buea, P. O. BOX 63, Buea Cameroon, February 1, 2008.
[6] Yang J., Some problems of Toeplitz operators on Bergman space of the unit ball (in Chinese), Dalian University of Technology, Dalian, 2009: 25-45.
[7] Cao G. F., Toeplitz operators on Dirichlet space (in Chinese), Chinese Annals of Mathematics, 2000, 21A(4): 499-512.
[8] Zhu K. H., Operator Theory in Function Spaces, M. Dekker, New York, 1990.
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脚注
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