一类拟微分算子的加权Morrey不等式  

Weighted Morrey Inequality for a Class of Pseudo-differential Operators

作　　者：邓宇龙 DENG Yu-long(School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105;Institute of Computational Mathematics,School of Science,Hunan University of Science and Engineering,Yongzhou 425199 China)

机构地区：[1]湘潭大学数学与计算科学学院,湖南湘潭411105 [2]湖南科技学院理学院,计算数学研究所,湖南永州425199

出　　处：《湘潭大学学报（自然科学版）》2020年第2期76-82,共7页Journal of Xiangtan University(Natural Science Edition)

基　　金：湖南省教育厅科学研究项目(18C1073)。

摘　　要：该文研究了一类象征a(x,ξ)属于L∞Sρ^m(R^n),ρ≤1的拟微分算子在加权Morrey空间Lω^p,κ(R^n)上的有界性问题,其中ω为Ap权.类似Kening和Staubach证明其Lp有界性的方法,该文获得了当q≥p时,如果m和p满足一定的条件,则拟微分算子在加权Morrey空间Lω^q,κ(R^n)上有界。In this paper,we study some sufficient conditions for the boundedness of a class of pseudo-differential operators T with symbols a(x,ξ)∈L∞ Sρ^m(R^n) and ρ≤1 on weighted Morrey spaces Lω^p,k(R^n),where ω∈A p.Namely,under some conditions of m and p,the pseudo-differential operators T are bounded on weighted Morrey spaces Lω^q,κ(R^n)for q≥p.Our proof follows Kening and Staubach’s method on L^p boundedness.

关 键 词：HARDY-LITTLEWOOD极大算子 拟微分算子 加权Morrey空间 

分 类 号：O175.3[理学—数学]