| 齐型空间上的Toeplitz型算子 |
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| 引用本文： | 谢佩珠,曹广福.齐型空间上的Toeplitz型算子[J].数学年刊A辑(中文版),2011,32(2):219-228. |
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| 作者姓名： | 谢佩珠 曹广福 |
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| 作者单位： | 中山大学数学与计算科学学院;广州大学数学与信息科学学院; |
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| 基金项目： | 国家自然科学基金(No.10971040)资助的项目 |
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| 摘 要： | 设X是齐型空间.设T_(j,1)和T_(j,2)是具有非光滑核的奇异积分算子,或者是±II(I是恒等算子).令Toeplitz型算子T_b=■T_(j,1)M_T_(j,2),其中M_bf(x)=b(x)f(x).研究了当b∈BMO(X)时,T_b(f)在加权情况下的有界性,以及当b∈BMO(X)时,与经典Carderon-Zygmund算子相联的T_b(f)在Morrey空间上的有界性.
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| 关 键 词： | Toeplitz算子 齐型空间 Morrey空间 BMO |
Toeplitz-type Operators on Homogeneous Type Spaces |
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| XIE Peizhu and CAO Guangfu.Toeplitz-type Operators on Homogeneous Type Spaces[J].Chinese Annals of Mathematics,2011,32(2):219-228. |
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| Authors: | XIE Peizhu and CAO Guangfu |
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| Institution: | XIE Peizhu~1 CAO Guangfu~2 1 School of Mathematics and Computational Science,Sun Yat-sen University,Guangzhou 510275,China.E-mail:xiepeizhu82@163.com 2 Corresponding author.College of Mathematics and Information Sciences,Guangzhou University,Guangzhou 510006,China. E-mail:guangfucao@163.com |
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| Abstract: | Let $X$ be a homogeneous type space. Let $T_{j,1}$ and $T_{j,2}$ be singular integral operators with non-smooth kernel,
or $\pm I$ ($I$ is the identity operator). Denote the Toeplitz-type operator by $T_b=\sum\limits_{j=1}^{N}T_{j,1}M_bT_{j,2}$, where $M_bf(x)=b(x)f(x)$.
In this paper, the weighted norm estimate of Toeplitz operator $T_b(f)$ related to singular
integral operators with non-smooth kernels is established when $b \in {\rm BMO}(X)$.
Moreover, when $b$ is a BMO function, the boundedness of Toeplitz operator $T_b(f)$ related to the standard
Carder\'on-Zygmund operator is discussed on Morrey spaces. |
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| Keywords: | Toeplitz operator Homogeneous type space Morrey space BMO |
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