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http://dx.doi.org/10.4134/JKMS.j170412

WEIGHTED VECTOR-VALUED BOUNDS FOR A CLASS OF MULTILINEAR SINGULAR INTEGRAL OPERATORS AND APPLICATIONS  

Chen, Jiecheng (Department of Mathematics Zhejiang Normal University)
Hu, Guoen (Department of Applied Mathematics Zhengzhou Information Science and Technology Institute)
Publication Information
Journal of the Korean Mathematical Society / v.55, no.3, 2018 , pp. 671-694 More about this Journal
Abstract
In this paper, we investigate the weighted vector-valued bounds for a class of multilinear singular integral operators, and its commutators, from $L^{p_1}(l^{q_1};\;{\mathbb{R}}^n,\;w_1){\times}{\cdots}{\times}L^{p_m}(l^{q_m};\;{\mathbb{R}}^n,\;w_m)$ to $L^p(l^q;\;{\mathbb{R}}^n,\;{\nu}_{\vec{w}})$, with $p_1,{\cdots},p_m$, $q_1,{\cdots},q_m{\in}(1,\;{\infty})$, $1/p=1/p_1+{\cdots}+1/p_m$, $1/q=1/q_1+{\cdots}+1/q_m$ and ${\vec{w}}=(w_1,{\cdots},w_m)$ a multiple $A_{\vec{P}}$ weights. Our argument also leads to the weighted weak type endpoint estimates for the commutators. As applications, we obtain some new weighted estimates for the $Calder{\acute{o}}n$ commutator.
Keywords
weighted vector-valued inequality; multilinear singular integral operator; commutator; non-smooth kernel; multiple weight;
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