张成国,姚祖喜.一类Hankel算子与Toeplitz算子的Sp性质[J].数学研究及应用,2006,26(1):14~18 |
一类Hankel算子与Toeplitz算子的Sp性质 |
The Sp Property of a kind of Hankel Operators and Toeplitz Operators |
投稿时间:2004-02-23 |
DOI:10.3770/j.issn:1000-341X.2006.01.003 |
中文关键词: 加权的Bergman空间 Toeplitz算子 Hankel算子 仿交换子 Schatten-von Neumann性质. |
英文关键词:M\"{o}ebius group weighted Bergman space Toeplitz operator Hankel operator paracommutator Schatten-von Neumann property. |
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中文摘要: |
对于$L^{\alpha ,2} \left( {D}\right)$的两类M\"{o}ebius不变子空间$A^{\alpha ,2} \left( {D}\right)$和$A^{\beta ,2} \left( {D} \right)$,我们定义了它们之间的Toeplitz算子$T_{f}^{s}$与其乘积空间上的Hankel算子$H_{f}^{r}$,并且研究了它们的有界性、紧性及Schatten-von Neumann性质. |
英文摘要: |
For two kind of M\"{o}ebius invariant subspace $A^{\alpha,2} \left( {D} \right)$ and $A^{\beta ,2} \left( {D} \right)$ of $L^{\alpha ,2} \left( {D} \right)$, define the Toeplitz operators $T_{f}^{s}$ and Hankel operators $H_{f}^{r} $ on $A^{\alpha ,2} \left({D} \right)\times A^{\beta ,2} \left( {D} \right)$ with an arbitrary analytic ``symbol function'' $f$ on a unit disk, and study their boundedness, compactness and Schatten-von Neumann properties. |
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