| 谢佩珠,曹广福.齐型空间上的Toeplitz型算子[J].数学年刊A辑,2011,32(2):219~228 |
| 齐型空间上的Toeplitz型算子 |
| Toeplitz-type Operators on Homogeneous Type Spaces |
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| DOI： |
| 中文关键词: Toeplitz算子 齐型空间 Morrey空间 BMO |
| 英文关键词:Toeplitz operator Homogeneous type space Morrey space BMO |
| 基金项目:国家自然科学基金(No.10971040)资助的项目 |
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| 中文摘要: |
| 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$\pm I$ ($I$是恒等算子).
令Toeplitz型算子$T_b=\sum\limits_{j=1}^{N}T_{j,1}M_bT_{j,2}$, 其中$M_bf(x)=b(x)f(x)$.
研究了当$b\in {\rm BMO}(X)$时, $T_b(f)$在加权情况下的有界性,
以及当$b\in {\rm BMO}(X)$时, 与经典Carder\'on-Zygmund算子相联的$T_b(f)$在Morrey空间上的有界性. |
| 英文摘要: |
| 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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