广义分数次积分交换子的有界性-应用数学专业论文.docxVIP

◆0，- ◆0，- 摘 摘 要 本文主要研究了广义分数次积分交换子的有界性．本文共分五章． 首先．我们介绍了广义分数次积分交换子的有界性的研究背景和研究结果．叙述 了在建立广义分数次积分交换子的有界性时所遇到的困难．克服这些困难的方法以 及主要结果． 第一章．我们讨论了【b．L—a12】和￡；“／2是从工n胁(舻)至IJBMO(R)上的有界算子，从 而推广了分数次积分交换子和分数次积分多线性交换子的有界性． 第二章．我们证明了由局部可积函数i=(6。，62 ．，b。)和广义分数次积分算子二一a／2(0 Qn)生成的多线性算子工i。72是从蜂(舻)至：ULip(。+卢一。／口)(俨)上的有界算子，也是 从Mq(Rn)到引订D(Rn)上的有界算子． 第三章．我们证明了由广义分数次积分算子L—n／2．具有标准核K的Calder6n-Zygmund 型算子及VMO函数生成的Toeplitz型算子是从1．2·1(舻)至rJL+，p(舻)上的有界算子，还进 一步讨论了在满足一定条件下，破∈VLq·p(BR)． 第四章．我们证明了由c8lder6n_zygmund型算子r和Lipschitz函数b∈二ip(口)(o 芦1)生成的交换子【6．T】在Lebesgue空间和几类Hardy型空间上的有界性． 第五章，在满足一定的消失条件下．我们证明了乘子分别在BMD(舻)，LMO(Rn) 和CBMOp_(舻)上的有界性． 关键词：多线性算子：广义分数次积分：Toeplitz型算子；BMO空间：消失．Morrey 空间：CalderSn-Zygmund型算子；乘子算子． -t 句 a恨 Abstractwe Abstract we study the boundedness of commutators of generalized fractional integrals· ituted with five chapters． First，we introduce the background and main results about commutators of generalized frac- tional integrals，we illustrate difficulties about establishing the boundedness of commutators of generalized fractional integrals，ideas to solve them and main results． In chapter 1，we discuss that fb．L一口／2】and工；叫2 bounded from扩／o(舻)into BMO(R”)． Respectively，the boundedness of commutator of fractional integral operator and the multflineal commutator of fractional integral essentially extended． In chapter 2，we establish the(．^绍，Lip(a+口一n／口))-boundedness and(Mg．BMO)·boundedness of the multilineal commutator Lio∥，which generated by finite family of locally integral functions 方=(b1，62 ．，6m)and the generalized fractional integral工咄／2 for 0Qn． In chapter 3．we prove that the Toeplitz-type operator e基generated by the generalized fractional integral，Calder6n-Zygmund operator with standald kernel K and VMO function is bounded from 1．2，^(舻)to Lq·p(舻)．We also show that e：，∈VLq泓(BR)，the vanishing-Morrey space，when it satisfies some conditions． In chapter 4，we establish the boundedness of the commutator【6．刁generated by Lipschitz function b∈Lip(口)(0卢1)and Calderdn-Zygmund type operator T t