Toeplitz Operators on Arveson and Dirichlet Spaces
Toeplitz Operators on Arveson and Dirichlet Spaces
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DOI：
10.1007/s00020-007-1493-1
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发表时间：
2007-04
影响因子：
0.8
通讯作者：
D. Alpay;H. Kaptanoğlu
中科院分区：
文献类型：
--
作者：
D. Alpay;H. Kaptanoğlu
我们在单位球上的所有Dirichlet空间上定义了Toeplitz算子，并发展了它们的基本性质。利用Carleson测度和Berezin变换刻画了具有正符号的有界、紧算子和Schatten类Toeplitz算子。我们的结果自然地推广了已知的加权Bergman空间的结果，一个特例适用于Arveson空间，并且我们在极限情况下恢复了经典的Hardy-空间Toeplitz算子，从而统一了所有这些空间上的Toeplitz算子的理论。我们将我们的算子应用于球的加权Bergman空间上的有界、紧和Schatten类加权复合算子的刻画。最后，我们研究了Toeplitz算子和移位算子之间的一些联系。
We define Toeplitz operators on all Dirichlet spaces on the unit ball ofand develop their basic properties. We characterize bounded, compact, and Schatten-class Toeplitz operators with positive symbols in terms of Carleson measures and Berezin transforms. Our results naturally extend those known for weighted Bergman spaces, a special case applies to the Arveson space, and we recover the classical Hardy-space Toeplitz operators in a limiting case; thus we unify the theory of Toeplitz operators on all these spaces. We apply our operators to a characterization of bounded, compact, and Schatten-class weighted composition operators on weighted Bergman spaces of the ball. We lastly investigate some connections between Toeplitz and shift operators.