Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (2): 313-325.

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Ap(φ) 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)

Abstract:

In this paper, we establish weighted Lp inequalities for pseudo-differential operators T and their commutators [b,T] with smooth symbols in Smρ,δ(Rn), where bBMO(Rn) and the weight ω belongs to the new class Ap(φ). It is well known that the Muckenhoupt class Ap falls within the class Ap(φ). This results extend the class of pseudo-differential operator to a wide range of m.

Key words: Pseudo-differential operator, Commutator, BMO, Ap(φ) weights, Weighted Lp estimate

CLC Number: 

  • O175.3
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