Please wait a minute...
高校应用数学学报
高校应用数学学报  2015, Vol. 30 Issue (2): 191-204    
    
一类奇异积分算子的Toeplitz算子的双权估计
曹美阳, 陈晓莉, 陈冬香
江西师范大学 数学与信息科学学院, 江西南昌 330022
Two weighted estimates for Toeplitz operators related to some singular integral
CAO Mei-yang, CHEN Xiao-li, CHEN Dong-xiang
Department of Mathematics, Jiangxi Normal University, Nanchang 330022, China
 全文: PDF 
摘要： 研究了与满足变形$L^{r}$-Hormander条件的奇异积分算子和加权Lipschitz函数生成的Toeplitz算子$T_{b}$的sharp极大函数的点态估计, 并应用该点态估计证明了Toeplitz算子$T_{b}$是从$L^{p}(w)$到$L^{q}(w^{1-q})$上的有界算子; 此外还建立了与变形Lipschitz条件的奇异积分算子和加权\text{BMO}函数相关的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$L^{p}(\mu)$到$L^{q}(\nu)$上的有界算子.
关键词： 变形$L^{r}$-Hormander条件;  变形Lipschitz条件;  Toeplitz算子;  双权估计    
Abstract: In this paper, the pointwise estimate for the sharp maximal function of the Toeplitz operators $T_{b}$ generalized by some singular integral whose kernel satisfied some variant $L^{r}$-Hormander condition and weighted Lipschitz function is established. The authors proved that $T_{b}$ is bounded from $L^{p}(w)$ to $L^{q}(w^{1-q})$. On the other hand, the pointwise estimate for the Toeplitz operator $T_{b}$ generalized by weighted \text{BMO} function and singular integral with a variant Lipschitz condition kernel is also established. Meanwhile the $(L^{p}(\mu),L^{q}(\nu))$-boundedness for $T_{b}$ is also proved.
Key words: variant $L^{r}$-Hormander condition    variant Lipschitz condition    Toeplitz operator    two weighted estimate
收稿日期: 2014-06-20 出版日期: 2018-06-05
CLC:  O174.2  
基金资助: 国家自然科学基金(11261023; 11461033; 11401269); 江西省自然科学基金(20142BAB201003)
服务　　
把本文推荐给朋友
加入引用管理器
E-mail Alert
RSS
作者相关文章　　
曹美阳
陈晓莉
陈冬香

引用本文:

曹美阳, 陈晓莉, 陈冬香. 一类奇异积分算子的Toeplitz算子的双权估计[J]. 高校应用数学学报, 2015, 30(2): 191-204.

CAO Mei-yang, CHEN Xiao-li, CHEN Dong-xiang. Two weighted estimates for Toeplitz operators related to some singular integral. Applied Mathematics A Journal of Chinese Universities, 2015, 30(2): 191-204.

链接本文:

http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2015/V30/I2/191

[1] 陈晓莉, 胡巧珍. 内蕴平方函数交换子在加权弱Hardy空间上的端点估计[J]. 高校应用数学学报, 2017, 32(1): 109-119.
[2] 陈冬香, 陈佩. 几类多线性算子在$B_\sigma$-Morrey空间上的有界性[J]. 高校应用数学学报, 2015, 30(3): 321-332.