奇异积分交换子在Hardy空间上的有界性

发布时间：2018-04-05 12:18

  本文选题：多线性交换子　切入点：Hardy空间　出处：《新疆大学》2017年硕士论文

【摘要】：调和分析是一门比较新的基础数学分支.它主要研究函数空间和算子并且在分析以及偏微分方程中占有相当重要的地位.对于每一个从事分析和偏微分方程研究的学者来说,它是不可或缺的知识和工具.Calder(?)n-Zygmund积分算子与Monge-Amp(?)re奇异积分算子作为调和分析中的经典算子,多年来一直广受学者们的追捧,并已经取得了许多成果.本文研究了由奇异积分算子T与Lipschitz函数bj(j = 1,·…,l)和BMO函数Bi(i = 1,…,m)生成的混合多线性交换子[(?),[(?),T]]在Lebesgue空间和Hardy上的有界性,其中(?) =(b1,…,bl),(?) =(B1,…,Bm).得到了该多线性交换子是Lp(Rn)到Lq(Rn)和(?)(Rn)到Ln/n-a(Rn)有界的,更进一步地证明了当m = 1时,该多线性交换子是H1(Rn)到(?)有界的.另外,本论文还讨论了 Monge-Amp(?)re奇异积分交换子在Lebesgue空间及Hardy空间上的有界性问题.设H为Monge-Amp(?)re奇异积分算子b∈LipF β 及1/q =1/p-β.交换子[b,H]是从 Lp(Rn,dμ)(1p1/β)到 以及从HFp(Rn)(1 +β)p≤1)到Lq(Rn,dμ)有界的.对于p = 1/(1 +β)时的端点情况,本文也给出了一个弱估计.具体来说,本论文主要由以下三章构成:第一章,主要阐述本文的研究的问题背景及文章结构.第二章,讨论了一类多线性交换子[(?),T]在Lebesgue和Hardy空间上的有界性.第三章,研究了交换子[(?),H]在Lebesgue和Hardy空间上的性质.
[Abstract]:Harmonic analysis is a relatively new branch of mathematics. It mainly studies the basic function of space and operator and occupies a very important position in the analysis and partial differential equations. For each analysis and partial differential equation research, it is an integral part of the knowledge and tools of.Calder (?) n-Zygmund integral operators and Monge-Amp (?) re singular integral operators as classical operators in harmonic analysis, over the years has been widely sought after by scholars, and has made a lot of achievements. This paper studied by singular integral operators T and Lipschitz function BJ (J = 1, and... L) and the BMO function Bi (I = 1,... M) generated mixed multilinear commutators [? (?), (?), T]]'s boundedness on Lebesgue space and Hardy, of which (?) = (B1,... BL), (?) = (B1,...) ,Bm).寰楀埌浜嗚�ュ�氱嚎鎬т氦鎹㈠瓙鏄疞p(Rn)鍒癓q(Rn)鍜，

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