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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2015, Vol. 30 Issue (2): 191-204    DOI:
    
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
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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     
Received: 20 June 2014      Published: 05 June 2018
CLC:  O174.2  
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CAO Mei-yang
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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.

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


一类奇异积分算子的Toeplitz算子的双权估计

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 
[1] CHEN Xiao-li, HU Qiao-zhen. Endpoint estimates for commutators of intrinsic square functions on the weighted weak Hardy spaces[J]. Applied Mathematics A Journal of Chinese Universities, 2017, 32(1): 109-119.
[2] CHEN Dong-xiang, CHEN Pei. The boundedness of some multilinear operators on  $B_\sigma$-Morrey spaces[J]. Applied Mathematics A Journal of Chinese Universities, 2015, 30(3): 321-332.