${A_{p}(\varphi)}$权, 拟微分算子及其交换子

数学物理学报 ›› 2021, Vol. 41 ›› Issue (2): 313-325.

${A_{p}(\varphi)}$权, 拟微分算子及其交换子

邓宇龙^1,²(),龙顺潮^2,*()

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

收稿日期:2020-05-03 出版日期:2021-04-26 发布日期:2021-04-29
通讯作者: 龙顺潮 E-mail:yuldeng@163.com;sclong@xtu.edu.cn
作者简介:邓宇龙, E-mail: yuldeng@163.com
基金资助:
湖南省教育厅科研项目(20A487);湖南省教育厅科研项目(18C107)

${A_{p}(\varphi)}$ Weights, Pseudo-Differential Operators and Their Commutators

Yulong Deng^1,²(),Shunchao Long^2,*()

¹ School of Mathematics Science, Changsha Normal University, Changsha 410100
² School of Mathematics and Computational Science, Xiangtan University, Hunan Xiangtan 411105

Received:2020-05-03 Online:2021-04-26 Published:2021-04-29
Contact: Shunchao Long E-mail:yuldeng@163.com;sclong@xtu.edu.cn
Supported by:
the Scientific Research Projects of Hunan Eduction Department(20A487);the Scientific Research Projects of Hunan Eduction Department(18C107)

摘要/Abstract

摘要：

该文探讨了象征函数属于Hörmander类$S^{m}_{\rho，\delta}(\mathbb{R}^n)$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$L^{p}_{\omega}(\mathbb{R}^n)$上的有界性问题，其中权$\omega$属于$A_{p}(\varphi)$，它包含了经典的Muckenhoupt权$A_{p}(\mathbb{R}^n)$.

关键词: 拟微分算子, 交换子, $BMO$, $A_{p}(\varphi)$权, 加权$L^{p}$估计

Abstract:

In this paper, we establish weighted $L^{p}$ inequalities for pseudo-differential operators $T$ and their commutators $[b, T]$ with smooth symbols in $S^{m}_{\rho, \delta}(\mathbb{R}^n)$, where $b\in BMO(\mathbb{R}^n)$ and the weight $\omega$ belongs to the new class $A_{p}(\varphi)$. It is well known that the Muckenhoupt class $A_{p}$ falls within the class $A_{p}(\varphi)$. This results extend the class of pseudo-differential operator to a wide range of $m$.

Key words: Pseudo-differential operator, Commutator, $BMO$, $A_{p}(\varphi)$ weights, Weighted $L^{p}$ estimate

中图分类号:

O175.3

邓宇龙,龙顺潮. ${A_{p}(\varphi)}$权, 拟微分算子及其交换子[J]. 数学物理学报, 2021, 41(2): 313-325.

Yulong Deng,Shunchao Long. ${A_{p}(\varphi)}$ Weights, Pseudo-Differential Operators and Their Commutators[J]. Acta mathematica scientia,Series A, 2021, 41(2): 313-325.

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