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

• 论文 • 上一篇    下一篇

${A_{p}(\varphi)}$权, 拟微分算子及其交换子

邓宇龙1,2(),龙顺潮2,*()   

  1. 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 Deng1,2(),Shunchao Long2,*()   

  1. 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:

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