几类较弱正则性的奇异积分算子及其交换子的有界性

发布时间：2018-03-19 15:48

本文选题：变形L~r-H(o|)rmander条件　切入点：变形Lipschitz条件　出处：《江西师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：本文研究了几类满足较弱正则性的奇异积分算子及其交换子的有界性,全文分为四章.第一章介绍了相关问题的背景资料和国内外研究现状,同时简单阐述了本文的来源与意义.第二章讨论了满足变形LrHormander条件的奇异积分算子的交换子在Lp空间上的有界性.第三章证明了满足变形Lipschitz条件的Toeplitz算子Tb从Lp(μ)到Lp(v)有界；同时,得到了满足变形Lr-Hormander条件的Toeplitz算子的双权估计.第四章研究了满足变形Lr-Hormander条件的奇异积分算子的高阶交换子TbT在加权Morrey空间上的有界性.
[Abstract]:In this paper, we study the boundedness of some singular integral operators and their commutators which satisfy the weak regularity. The whole paper is divided into four chapters. In chapter 2, we discuss the boundedness of commutators of singular integral operators satisfying deformed LrHormander condition in LP space. In Chapter 3, we prove that the Toeplitz operator TB satisfying the deformed Lipschitz condition is bounded from LP (渭) to LP v. In chapter 4th, we study the boundedness of higher order commutator TbT of singular integral operators satisfying deformed Lr-Hormander condition on weighted Morrey spaces.
【学位授予单位】：江西师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O177

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