Weighted Oscillation and Variation Inequalities for Singular Integrals and Commutators Satisfying Hrmander Type Conditions

作     者：Jing ZHANG Huo Xiong WU 

作者机构：School of Mathematics and Statistics Yili Normal College Yining 835000 P. R. China School of Mathematical Sciences Xiamen University Xiamen 361005 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2017年第33卷第10期

页      面：1397-1420页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the NNSF of China(Grant Nos.11371295 and 11471041) the NSF of Fujian Province of China(Grant No.2015J01025) Foundation for Doctors of Yili Normal College(Grant No.2017YSBS09) 

主　　题：Oscillation variation singular integrals commutators BMO functions HSrmander con-ditions Muckenhoupt weights 

摘      要：This paper is devoted to investigating the weighted LP-mapping properties of oscillation and variation operators related to the families of singular integrals and their commutators in higher dimension. We establish the weighted type （p, p） estimates for 1 〈 p 〈 ∞ and the weighted weak type （1, 1） estimate for the oscillation and variation operators of singular integrals with kernels satisfying certain HSrmander type conditions, which contain the Riesz transforms, singular integrals with more general homogeneous kernels satisfying the Lipschitz conditions and the classical Dini＇s conditions as model examples. Meanwhile, we also obtain the weighted LP-boundeness for such operators associated to the family of commutators generated by the singular integrals above with BMO（Rd）-functions.