【作者】 邹丹；

【导师】 陈冬香；

【作者基本信息】 江西师范大学 ， 基础数学， 2014， 硕士

【摘要】 本学位论文主要研究了与Schrodinger算子相关的几类算子及其交换子的有界性.行文结构安排如下：第一章介绍了Schrodinger算子和Marcinkiewicz积分及其交换子的研究背景和国内外的主要结果以及本文选题的来源与意义.第二章研究了与schrodinger算子相关的Marcinkiewicz积分及其交换子的有界性.第三章研究了与Schrodinger算子相关的Marcinkiewicz积分在Morrey空间的估计.第四章研究了与高阶Schrodinger算子相关的Riesz变换及其交换子的Lp估计.更多还原

【Abstract】 In this recent paper, we study the boundedness of some operators of Schrodinger operator type and their commutators. The paper is constituted with four chapters.In chapter1, we introduce the background and main results about Schrodinger operator and Marcinkiewicz integral operator and its commutator. Besides, we also simply illustrate how and why these topics come out.In chapter2, we present the boundedness of Marcinkiewicz integral of Schrodinger operator type and its commutator.In chapter3, we consider the estimates of Marcinkiewicz integral of Schrodinger operator type on morrey spaces.In chapter4, we discuss LP estimates of higher order Riesz transform related to Schrodinger type operators and their commutators.更多还原