变指标分数次Hardy算子的高阶交换子

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1、分类号：o174.2密级：公开学校代码：11065学号：2015020210学术硕士学位论文变指标分数次Hardy算子的高阶交换子作者姓名于云凤指导教师赵凯教授学科应用数学培养单位数学与统计学院答辩日期2018年5月19日摘要论文介绍了与变指数函数空间相关的一些基本概念、引理和与Hardy算子相关的一些定义及基本性质,基于这些性质和重要引理,利用H¨older不等式和Jensen不等式,首先证明了变指标分数次Hardy算子及其共轭算子与BMO函数生成的高阶交换子在变指数Herz-Morrey空间上的有界性,这里的变指数Herz-

2、Morrey空间只有一个变化的指数.其次证明了变指标分数次Hardy算子及其共轭算子与Lipschitz生成的高阶交换子在变指数Herz-Morrey空间上的有界性,这里的变指数Herz-Morrey空间有两个变化的指数.关键词:Hardy算子;变指数;BMO函数;Lipschitz函数;Herz-Morrey空间;有界性AbstractInthisthesis,weintroducedsomebasicconceptsandlemmasoffunctionspaceswithvariableexponents,andsomed

3、efinitionsandpropertiesrelatedtoHardyoperators.Then,basedonthesepropertiesandimportantlemmas,byusingtheJensenandH¨olderinequali-ties,weestablishedtheboundednessofthehighercommutatorsgeneratedby𝑛-dimensionalfractionalHardyoperatorsandtheirconjugateoperatorsofvariableo

4、rderandBMOfunc-tionsontheHerz-Morreyspaceswithonlyonevariableexponent.Atlast,weobtainedtheboundednessofthehighercommutatorsgeneratedby𝑛-dimensionalfractionalHardyoperatorsandtheirconjugateoperatorsofvariableorderandLipschitzfunctionsontheHerz-Morreyspaceswithtwovaria

5、bleexponents.Keywords:Hardyopertator;variableexponent;BMOspace;Lipschitzspace;Herz-Morreyspace;boundedness目录引引引言言言························································································1第第第一一一章章章基基基础础础知知知识识识···········································

6、··························31.1基本概念···········································································31.2主要引理与命题···