与非光滑核的奇异积分相关的Toeplitz算子的双权估计

数学物理学报 ›› 2013, Vol. 33 ›› Issue (6): 1122-1132.

与非光滑核的奇异积分相关的Toeplitz算子的双权估计

陈冬香|李倩丽

江西师范大学数学与信息科学学院南昌 |330022

收稿日期:2012-08-07 修回日期:2013-10-24 出版日期:2013-12-25 发布日期:2013-12-25
基金资助:
国家自然科学基金(10961015, 11261023)、江西省自然科学基金(20122BAB201011)和江西省教育厅基金(GJJ10397)资助

Two Weighted Estimates for Toeplitz Operator Related to Singular Integrals Operator with Non-smooth Kernels

CHEN Dong-Xiang, LI Qian-Li

College of Mathematics and Information, Jiangxi Normal University, Nanchang 330022

Received:2012-08-07 Revised:2013-10-24 Online:2013-12-25 Published:2013-12-25
Supported by:
国家自然科学基金(10961015, 11261023)、江西省自然科学基金(20122BAB201011)和江西省教育厅基金(GJJ10397)资助

摘要/Abstract

摘要：

研究了与非光滑核的奇异积分算子和加权Lipschitz函数相关的的Toeplitz算子T_b的sharp极大函数的点态估计, 并应用该估计证明了Toeplitz算子T_b是从L^p(ω)到L^q(ω^1-q)上的有界算子. 此外还建立了与非光滑核的奇异积分算子和加权BMO函数相关的的Toeplitz算子T_b的sharp极大函数的点态估计, 证明了这类Toeplitz算子是从L^p(μ)到L^q(ν)上的有界算子.

关键词: Toeplitz 算子, 加权Lipschitz空间, 加权BMO空间, 双权估计

Abstract:

This paper is concerned with pointwise estimates for the sharp maximal function of the Toeplitz operators T_b related to singular integral operators with non-smooth kernel and a weighted Lipschitz function. We show that Toeplitz operator T_b is bounded from L^p(ω) to L^q(ω^1-q). On the other hand, we also establish pointwise estimates for the sharp maximal function of the Toeplitz operator related to singular integral operators with non-smooth kernel and a weighted BMO function and show that this Toeplitz operator T_b is bounded from L^p(μ) to L^p(ν).

Key words: Toeplitz operator, Weighted Lipschitz spaces, Weighted BMO(ω) space, Two weighted estimate

中图分类号:

42B25

陈冬香, 李倩丽. 与非光滑核的奇异积分相关的Toeplitz算子的双权估计[J]. 数学物理学报, 2013, 33(6): 1122-1132.

CHEN Dong-Xiang, LI Qian-Li. Two Weighted Estimates for Toeplitz Operator Related to Singular Integrals Operator with Non-smooth Kernels[J]. Acta mathematica scientia,Series A, 2013, 33(6): 1122-1132.

[1]	夏锦, 王晓峰, 曹广福. Dirichlet空间上Toeplitz算子的一些性质[J]. 数学物理学报, 2012, 32(2): 395-403.
[2]	周肖沙, 刘岚喆. 向量值多线性算子的加权Lipschitz估计[J]. 数学物理学报, 2011, 31(4): 930-945.