Bochner-Riesz算子及其高阶交换子L^p有界的必要条件  

Necessary Condition Boundedness of Bochner-Riesz Operator and Its Higher Commutators

作　　者：夏霞[1] 

机构地区：[1]天津师范大学数学科学学院,天津300387

出　　处：《应用泛函分析学报》2009年第4期377-382,共6页Acta Analysis Functionalis Applicata

基　　金：国家自然科学基金(10971141);北京市自然科学基金(1092004);天津师范大学引进人才基金(5RL067)

摘　　要：通过选择适当的Lp函数并应用连续分解方法,给出了低于临界阶的Bochner-Riesz算子在Lp空间有界的新的证明,同时得到了该算子和Lipschitz函数构成的高阶交换子Lp有界性的必要条件.In terms of continuous decomposition and choosing an appropriate L^p function, the author poses a new method to prove the necessary condition for L^p boundedness of Bochner-Riesz operators below the critical index. And a similar necessary condition for L^p-boundedness of higher order commutators generated by Bochner-Riesz operators below the critical index and Lipschitz functions is obtained by this method.

关 键 词：低于临界阶的Bochner-Riesz算子 交换子 LIPSCHITZ函数 Lp空间 

分 类 号：O177.6[理学—数学]