首页 | 本学科首页   官方微博 | 高级检索  
     检索      

与强奇异 Calder\'{o}n-Zygmund算子相关的Toeplitz算子的双权估计
引用本文: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(中文版),2013,34(2):167-178.
作者姓名:陈冬香  毛素珍
作者单位:江西师范大学数学与信息科学学院, 南昌 330022.;江西师范大学数学与信息科学学院, 南昌 330022.
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)
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.

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

Two Weighted Estimates of Toeplitz Operator Related to Strongly Singular Calder\'{o}n-Zygmund Operators
CHEN Dongxiang and MAO Suzhen.Two Weighted Estimates of Toeplitz Operator Related to Strongly Singular Calder\''{o}n-Zygmund Operators[J].Chinese Annals of Mathematics,2013,34(2):167-178.
Authors:CHEN Dongxiang and MAO Suzhen
Institution:College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China.;College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China.
Abstract: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.
Keywords:
点击此处可从《数学年刊A辑(中文版)》浏览原始摘要信息
点击此处可从《数学年刊A辑(中文版)》下载免费的PDF全文
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号