Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2017.06.18
  • Accepted : 2017.10.25
  • Published : 2018.05.01
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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

Acknowledgement

Supported by : NNSF of China

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