TY - JOUR AU - Chen, Dongxiang AU - Huang, Anzhi PY - 2017 TI - Endpoint estimates for commutators of mutilinear square function satisfying some integrable condition JO - Journal of Nonlinear Sciences and Applications SP - 4846--4865 VL - 10 IS - 9 AB - 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. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.010.09.26 DO - 10.22436/jnsa.010.09.26 ID - Chen2017 ER -