本文選題：單邊C-Z奇異積分 + 單邊權(quán)��； 參考：《山東師范大學(xué)》2015年碩士論文

【摘要】：近半個(gè)世紀(jì)以來(lái),現(xiàn)代調(diào)和分析理論取得了許多重大進(jìn)展,其思想、方法和技巧在很多數(shù)學(xué)領(lǐng)域中得到廣泛的應(yīng)用.以Calderon-Zygmund(C-Z)奇異積分算子為代表的算子理論自創(chuàng)立以來(lái),便在調(diào)和分析中處于中心地位.本文主要研究有關(guān)變形核的單邊C-Z奇異積分算子的加權(quán)估計(jì),單邊Cohen型奇異積分算子交換子在加權(quán)Triebel-Lizorkin空間的Lipschitz估計(jì),以及在單邊加權(quán)Morrey空間中滿足一定尺寸條件的單邊次線性算子的有界性.本文的主要內(nèi)容安排如下：在第一章中,我們將內(nèi)容分為六個(gè)小節(jié).首先主要介紹有關(guān)核函數(shù)的奇異積分算子的研究背景和研究現(xiàn)狀.然后給出了經(jīng)典的C-Z理論和Ap權(quán)函數(shù)的定義和雙邊情形下變形的Hormander條件.其次引入單邊權(quán)函數(shù)和單邊C-Z奇異積分算子及其交換子的定義及性質(zhì).接下來(lái)主要討論本文中用到的幾類單邊函數(shù)空間的定義形式和將要用到的一些必要引理.最后簡(jiǎn)單的介紹本文的主要研究工作.在第二章中,我們首先給出滿足變形的Lipschitz條件的單邊C-Z奇異積分算子T+的定義.然后,以單邊sharp極大函數(shù)為橋梁來(lái)求得此類單邊奇異積分算子的加權(quán)Lp(p1)有界性.對(duì)于p=1時(shí),運(yùn)用單邊C-Z分解來(lái)完成單邊奇異積分算子T+的弱(1,1)有界性估計(jì).第三章分成兩個(gè)主要的部分.我們主要利用單邊權(quán)的外推方法,來(lái)分別討論單邊Cohen型奇異積分算子交換子和分?jǐn)?shù)次積分算子交換子在單邊加權(quán)Triebel-Lizorkin空間的Lipschitz的有界性估計(jì).在第四章中,首先介紹了滿足一定尺寸條件的單邊次線性算子和單邊分?jǐn)?shù)次積分算子.然后在單邊加權(quán)Morrey空間中討論這兩類單邊算子的有界性.
[Abstract]:In the last half century, modern harmonic analysis theory has made great progress, and its ideas, methods and techniques have been widely used in many fields of mathematics. The operator theory, represented by Calderon-Zygmund C-Z) singular integral operator, has been at the center of harmonic analysis since it was founded. In this paper, we mainly study the weighted estimates of one-sided C-Z singular integral operators with deformed kernels and the Lipschitz estimates of commutators of one-sided Cohen type singular integral operators in weighted Triebel-Lizorkin spaces. And the boundedness of unilateral sublinear operators satisfying certain size conditions in one-sided weighted Morrey spaces. The main contents of this paper are as follows: in the first chapter, we divide the content into six sections. Firstly, the research background and present situation of singular integral operators for kernel functions are introduced. Then, the classical C-Z theory and the definition of AP weight function and the Hormander condition of deformation in bilateral case are given. Secondly, the definition and properties of one-sided weight function, one-sided C-Z singular integral operator and its commutator are introduced. Then we mainly discuss the definition form and necessary Lemma of several kinds of unilateral function spaces used in this paper. Finally, the main research work of this paper is briefly introduced. In chapter 2, we first give the definition of one-sided C-Z singular integral operator T which satisfies the Lipschitz condition of deformation. Then, we use the one-sided sharp maximal function as the bridge to obtain the weighted LpP-1) boundedness of this singular integral operator. For p = 1, the one-sided C-Z decomposition is used to complete the weakly bound estimate of one-sided singular integral operator T. Chapter three is divided into two main parts. We mainly use the one-sided weight extrapolation method to discuss the boundedness estimates of the Lipschitz of singular integral operator commutators of one-sided Cohen type and fractional integral operator commutators in one-sided weighted Triebel-Lizorkin spaces, respectively. In the fourth chapter, we first introduce the unilateral sublinear operator and the unilateral fractional integral operator which satisfy certain size conditions. Then we discuss the boundedness of these two kinds of one-sided operators in one-sided weighted Morrey spaces.
【學(xué)位授予單位】：山東師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：O177

【參考文獻(xiàn)】

相關(guān)期刊論文 前2條

1 Yong DING;Shan Zhen LU;K，

本文編號(hào)：1982966