Endpoint estimates for commutators of mutilinear square function satisfying some integrable condition
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Authors
Dongxiang Chen
- Department of Mathematic and information Science, Jiangxi Normal University, Nanchang, China.
Anzhi Huang
- Department of Mathematic and information Science, Jiangxi Normal University, Nanchang, China.
Abstract
In this paper, the \((L^{p_1}\times\cdots\times L^{p_m},L^q)\)-estimate for the commutator \(T_{\Pi b}\) generalized by multilinear square function \(T\)
and Lipschitz function \(\vec{b}\) is established for \(\frac{1}{q}=\sum_{j=1}^m\frac{1}{p_i}-\frac{\beta}n,~ p_i>p_0\ge1\).
Meanwhile, we also establish \((L^{p_1}\times\cdots\times L^{p_m}, \dot{\Lambda}_{\beta-\frac{n}p} )\)-boundedness
and \((L^{\frac{n}{\beta_1}}\times\cdots\times L^{\frac{n}{\beta_m}},BMO)\)-estimates for the commutator \(T_{\Pi b}\). Finally, the \((L^{p_1}\times\cdots\times L^{p_m}, \dot{F}_{p}^{\beta,\infty})\)-boundedness is obtained, too.
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ISRP Style
Dongxiang Chen, Anzhi Huang, Endpoint estimates for commutators of mutilinear square function satisfying some integrable condition, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 9, 4846--4865
AMA Style
Chen Dongxiang, Huang Anzhi, Endpoint estimates for commutators of mutilinear square function satisfying some integrable condition. J. Nonlinear Sci. Appl. (2017); 10(9):4846--4865
Chicago/Turabian Style
Chen, Dongxiang, Huang, Anzhi. "Endpoint estimates for commutators of mutilinear square function satisfying some integrable condition." Journal of Nonlinear Sciences and Applications, 10, no. 9 (2017): 4846--4865
Keywords
- Multilinear square function
- iterated commutator
- Lipschitz space
- Triebel-Lizorkin space.
MSC
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