本文選題：多線性交換子　切入點(diǎn)：Hardy空間　出處：《新疆大學(xué)》2017年碩士論文

【摘要】：調(diào)和分析是一門比較新的基礎(chǔ)數(shù)學(xué)分支.它主要研究函數(shù)空間和算子并且在分析以及偏微分方程中占有相當(dāng)重要的地位.對(duì)于每一個(gè)從事分析和偏微分方程研究的學(xué)者來說,它是不可或缺的知識(shí)和工具.Calder(?)n-Zygmund積分算子與Monge-Amp(?)re奇異積分算子作為調(diào)和分析中的經(jīng)典算子,多年來一直廣受學(xué)者們的追捧,并已經(jīng)取得了許多成果.本文研究了由奇異積分算子T與Lipschitz函數(shù)bj(j = 1,·…,l)和BMO函數(shù)Bi(i = 1,…,m)生成的混合多線性交換子[(?),[(?),T]]在Lebesgue空間和Hardy上的有界性,其中(?) =(b1,…,bl),(?) =(B1,…,Bm).得到了該多線性交換子是Lp(Rn)到Lq(Rn)和(?)(Rn)到Ln/n-a(Rn)有界的,更進(jìn)一步地證明了當(dāng)m = 1時(shí),該多線性交換子是H1(Rn)到(?)有界的.另外,本論文還討論了 Monge-Amp(?)re奇異積分交換子在Lebesgue空間及Hardy空間上的有界性問題.設(shè)H為Monge-Amp(?)re奇異積分算子b∈LipF β 及1/q =1/p-β.交換子[b,H]是從 Lp(Rn,dμ)(1p1/β)到 以及從HFp(Rn)(1 +β)p≤1)到Lq(Rn,dμ)有界的.對(duì)于p = 1/(1 +β)時(shí)的端點(diǎn)情況,本文也給出了一個(gè)弱估計(jì).具體來說,本論文主要由以下三章構(gòu)成:第一章,主要闡述本文的研究的問題背景及文章結(jié)構(gòu).第二章,討論了一類多線性交換子[(?),T]在Lebesgue和Hardy空間上的有界性.第三章,研究了交換子[(?),H]在Lebesgue和Hardy空間上的性質(zhì).
[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?jiǎn)璇ュ绾挎�т氦鎹㈠瓙鏄疞p(Rn)鍒癓q(Rn)鍜，

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