拟微分算子交换子的端点估计  

Endpoint Estimates for Commutators of Pseudo differential Operators

作　　者：邓宇龙 龙顺潮[2] Yu Long DENG;Shun Chao LONG(School of Mathematical Sciences,Changsha Normal University,Changsha 410100,P.R.China;School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105,P.R.China)

机构地区：[1]长沙师范学院数学科学学院,长沙410100 [2]湘潭大学数学与计算科学学院,湘潭411105

出　　处：《数学学报（中文版）》2022年第2期309-316,共8页Acta Mathematica Sinica：Chinese Series

基　　金：湖南省教育厅科研项目(20A487)。

摘　　要：本文给出了象征属于Hörmander类S^(m)_(ρ,δ)(R^(n))的拟微分算子T的交换子[b,T]从H^(1)(R^(n))到弱L^(1)(R^(n))以及H^(1)_(b)(R^(n))到L^(p)(R^(n))的有界性估计,其中b∈BMO(R^(n)).In this paper,we establish two endpoint estimates for the commutator,[b,T],of a class of pseudodifferential operators T with symbols in Hörmander class S^(m)_(ρ,δ)(R^(n)).The first one is that the commutator[b,T]is bounded from Hardy space H^(1)(R^(n))into weak L^(1)(R^(n))space.The second one is an estimate in the Hardy type spaces associated with b,where b∈BMO(R^(n)).

关 键 词：拟微分算子 交换子 HARDY空间 弱L^(1)(R^(n))空间 

分 类 号：O175.3[理学—数学]