关于格林算子和同伦算子的复合算子的双权Ponincaré范数不等式(英文)  

The two weighted Poincaré norm inequalities for the composition of Green operator and homotopy operator

作　　者：李华灿[1] 邢宇明[2] 李群芳 

机构地区：[1]江西理工大学理学院,赣州341000 [2]哈尔滨工业大学数学系,哈尔滨150001 [3]赣州师范高等专科学校数学系,赣州341000

出　　处：《黑龙江大学自然科学学报》2014年第4期484-489,共6页Journal of Natural Science of Heilongjiang University

基　　金：Supported by the Youth Foundation of Jiangxi Provincial Education Department(GJJ13376);the Foundation of the Jiangxi University of Science and Technology(jxxj12073)

摘　　要：基于格林算子的Lp有界性和微分形式的嵌入不等式,证明有界域Ω上关于格林算子和同伦算子的复合算子的Poincaré不等式;通过令u=d*v,得到作用于共轭A-调和张量的复合算子TG的Poincaré-型范数估计。借助于Hlder不等式和Ar(λ,Ω)-权性质的巧妙结合,给出Ar(λ,Ω)-双权的Poincaré-型积分不等式。Based on the results of the L^p boundedness of Green＇s operator and the imbedding inequality acting on differential forms,the Poincaré inequalities for the composition of Green＇s operator G and the Homotopy operator T on the bounded domain Ω are proven. Thereby,the Poincaré-type norm estimation for the composition of G and T acted on the conjugate A-harmonic tensors is achieved by selecting u = d＊v. At last,by using the Hlder inequlity and the property of the Ar（ λ,Ω）-weight,the Ar（ λ,Ω）-two weighted Poincaré integral inequalities are given.

关 键 词：范数不等式 同伦算子 共轭A-调和张量 Ar(λ Ω)-双权 

分 类 号：O175.2[理学—数学]