| 陈冬香,毛素珍.与强奇异 Calder\'{o}n-Zygmund算子相关的Toeplitz算子的双权估计[J].数学年刊A辑,2013,34(2):167~178 |
| 与强奇异 Calder\'{o}n-Zygmund算子相关的Toeplitz算子的双权估计 |
| Two Weighted Estimates of Toeplitz Operator Related to Strongly Singular Calder\'{o}n-Zygmund Operators |
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| DOI： |
| 中文关键词: 加权BMO$(\omega)$空间,
加权Lipschitz函数空间, 强奇异Calder\'{o}n-Zygmund算子,
Toeplitz算子, Sharp极大函数 |
| 英文关键词:Weighted BMO(ω) space, Weighted Lipschitz space, Strongly Calder′on-Zygmund operator, Toeplitz operator, Sharp maximal |
| 基金项目:国家自然科学基金 (No.10961015, No.10871173, No.11261023), 江西省自然科学基金(No.20122BAB201011) ,江西省教育厅基金(No.GJJ10397, No.GJJ12203) |
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| 中文摘要: |
| 研究了与强奇异Calder\'{o}n-Zygmund算子和加权
Lipschitz函数${\rm Lip}_{\beta_0,\omega}$相关的Toeplitz算子$T_b$的sharp极大函数的点态估计,并证明了Toeplitz算子是从
$L^p(\omega)$到$L^q(\omega^{1-q})$上的有界算子.此外, 建立了与强奇异Calder\'{o}n-Zygmund算子和加权
BMO函数${\rm BMO}_{\omega}$相关的Toeplitz算子$T_b$的sharp极大函数的点态估计,并证明了Toeplitz算子是从
$L^p(\mu)$到$L^q(\nu)$上的有界算子.上述结果包含了相应交换子的有界性. |
| 英文摘要: |
| In this paper, the authors concern the
pointwise estimates of the sharp maximal function of the Toeplitz operator $T_b$ related
to strongly singular
Calder\'{o}n-Zygmund operators and the weighted Lipschitz spaces ${\rm Lip}_{\beta_0,\omega}$. The authors show that the Toeplitz operator $T_b$ is bounded from
$L^p(\omega)$ to $L^q(\omega^{1-q}).$ On the other hand, the aurthors also establish the pointwise
estimates of the sharp maximal function of
the Toeplitz operator $T_b$ related to the strongly singular
Calder\'{o}n-Zygmund operators and the weighted ${\rm BMO}$ spaces ${\rm BMO}(\omega)$,
and show that The Toeplitz operator $T_b$ is bounded from
$L^p(\mu)$ to $L^p(\nu).$ The above results imply the boundedness of the corresponding commutators. |
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