L^2（R^n） Boundedness for a Class of Multilinear Singular Integral Operators

作     者：GuoEnHU 

作者机构：DepartmentofAppliedMathdematicsUniversityofInformationEngineeringP.O.Box1001-747Zhengzhou450002P.R.China 

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

年 卷 期：2003年第19卷第2期

页      面：397-404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：国家自然科学基金 

主　　题：Multilinear singular integral operator BMO(ℝ n ) Fourier transform estimate 42B20 

摘      要：The L^2(A^n) boundedness for the multilinear singular integral operators defined by$T_A f\left( x \right) = \int_{Ropf^n } {{{\Omega \left( {x - y} \right)} \over {\left| {x - y} \right|^{n + 1} }}} \left( {A\left( x \right) - A\left( y \right) - \nabla A\left( y \right)\left( {x - y} \right)} \right)f\left( y \right)dy$is considered, whereQ is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one, A has derivatives of order one in BMO(A^n). A sufficient condition based on the Fourier transform estimate and implying the L^2(A^n) boundedness for the multilinear operator TA is given.