A_(p)(φ)权,拟微分算子及其交换子  

A_(p)(φ)Weights,Pseudo-Differential Operators and Their Commutators

作　　者：邓宇龙 龙顺潮[2] Deng Yulong;Long Shunchao(School of Mathematics Science,Changsha Normal University,Changsha 410100;School of Mathematics and Computational Science,Xiangtan University,Hunan Xiangtan 411105)

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,湖南湘潭411105

出　　处：《数学物理学报（A辑）》2021年第2期313-325,共13页Acta Mathematica Scientia

基　　金：湖南省教育厅科研项目(20A487,18C1073)。

摘　　要：该文探讨了象征函数属于Hoormander类S_(ρ,δ)^(m)(R^(n))的拟微分算子T及其与BMO函数b生成的交换子[b,T]在加权L^(p)空间L_(w)^(p)(R^(n))上的有界性问题,其中权w属于A_(p)(φ),它包含了经典的Muckenhoupt权A_(p)(R^(n)).In this paper,we establish weighted L^(p)inequalities for pseudo-differential operators T and their commutators[b,T]with smooth symbols in S_(ρ,δ)^(m)(R^(n)),where b∈BMO(R^(n))and the weightωbelongs to the new class A_(p)(φ).It is well known that the Muckenhoupt class A_(p)falls within the class A_(p)(φ).This results extend the class of pseudo-differential operator to a wide range of m.

关 键 词：拟微分算子 交换子 BMO A_(p)(φ)权 加权L^(p)估计 

分 类 号：O175.3[理学—数学]