%0 Journal Article %T Endpoint estimates for commutators of mutilinear square function satisfying some integrable condition %A Chen, Dongxiang %A Huang, Anzhi %J Journal of Nonlinear Sciences and Applications %D 2017 %V 10 %N 9 %@ ISSN 2008-1901 %F Chen2017 %X 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. %9 journal article %R 10.22436/jnsa.010.09.26 %U http://dx.doi.org/10.22436/jnsa.010.09.26 %P 4846--4865 %0 Journal Article %T On commutators of singular integrals and bilinear singular integrals %A R. R. Coifman %A Y. Meyer %J Trans. Amer. Math. Soc. %D 1975 %V 212 %F Coifman1975 %0 Book %T Au-delà des opérateurs pseudo-différentiels %A R. R. Coifman %A Y. Meyer %D 1978 %I Societe mathematique de France %C Paris %F Coifman1978 %0 Journal Article %T Commutateurs díntégrales singuliéres et opérateurs multilineaires %A R. R. Coifman %A Y. Meyer %J Ann. Inst. Fourier %D 1978 %V 28 %F Coifman1978 %0 Journal Article %T Multilinear Littlewood-Paley estimates with applications to partial differential equations %A E. B. Fabes %A D. S. Jerison %A C. E. Kenig %J Proc. Natl. Acad. Sci. %D 1982 %V 79 %F Fabes1982 %0 Journal Article %T Necessary and sufficient conditions for absolute continuity of elliptic harmonic measure %A E. B. Fabes %A D. S. Jerison %A C. E. Kenig %J Ann. of Math. %D 1984 %V 119 %F Fabes1984 %0 Journal Article %T Multilinear square functions and partial differential equations %A E. B. Fabes %A D. S. Jerison %A C. E. Kenig %J Amer. J. Math. %D 1985 %V 107 %F Fabes1985 %0 Journal Article %T Some maximal inequalities %A C. Fefferman %A E. Stein %J Amer. J. Math. %D 1971 %V 93 %F Fefferman1971 %0 Journal Article %T On multilinear fractional integrals %A L. Grafakos %J Studia Math. %D 1992 %V 102 %F Grafakos 1992 %0 Journal Article %T Maximal operator and weighted norm inequalities for multilinear singular integrals %A L. Grafakos %A R. H. Torres %J Indiana Univ. Math. J. %D 2002 %V 51 %F Grafakos2002 %0 Journal Article %T Multilinear Calderon-Zygmund theory %A L. Grafakos %A R. Torres %J Adv. Math. %D 2002 %V 165 %F Grafakos2002 %0 Journal Article %T Multilinear estimates and fractional integration %A C. E. Kenig %A E. M. Stein %J Math. Res. Lett. %D 1999 %V 6 %F Kenig1999 %0 Journal Article %T New maximal functions and multiple weight for the multilinear Caldeón-Zygmund theory %A A. K. Lerner %A S. Ombrosi %A C. Pérez %A R. H. Torres %A R. Trujillo-Gonzszlez %A %J Advances in Mathematics %D 2009 %V 220 %F Lerner2009 %0 Journal Article %T Weighted version of Carleson measure and multilinear Fourier multiplier %A W. Li %A Q.-G. Xue %A K. Yabuta %J Forum Math. %D 2015 %V 27 %F Li2015 %0 Journal Article %T Characterization of the Besov spaces via the commutator operator of Coifman Rochberg and Weiss %A M. Paluszynski %J Indiana Univ Math J. %D 1995 %V 44 %F Paluszynski1995 %0 Journal Article %T On the boundedness of multilinear Littlewood-Paley \(g^*_\lambda\) function %A S. Shi %A Q. Xue %A K. Yabuta %J J. Math. Pures Appl. %D 2014 %V 101 %F Shi2014 %0 Journal Article %T Endpoint estimates for multilinear fractional integrals %A L. Tang %J J. Aust. Math. Soc. %D 2008 %V 84 %F Tang2008 %0 Journal Article %T On multilinear square function and its applications to multilinear Littlewood-Paley operators with nonconvolution type kernels %A Q. Xue %A J. Yan %J J. Math. Anal. Appl. %D 2015 %V 422 %F Xue2015 %0 Journal Article %T A multilinearization of Littlewood-Paley’s g-function and Carleson measures %A K. Yabuta %J Tohoku Math. J. %D 1982 %V 34 %F Yabuta1982