Boundedness of certain integral operators with rough kernels

本学位论文研究沿低维集的粗糙核~Marcinkiewicz~积分算子、多参数奇异积分算子以及多线性奇异积分算子及其交换子的有界性.全文共分七章： 第一章概述本文所研究问题的背景以及国内外研究现状,并简单介绍 本文的主要结果与结构安排. 第二章讨论当积分核满足$\Omega\in\mathcal{F}_{\beta}(S^{n-1})\,(n\geq2)$时,沿多项式复合子流形的抛物型Marcinkiewicz积分算子的$L^p$有 界性,这些结果本质上改进和推广了一些已有的结果.并在主要结果的证明过程中给出了一个系统的处理方法. 第三章考虑带径向粗糙核的沿多项式复合曲线的...This thesis is devoted to studying the $L^p$ bounds for rough Marcinkiewicz integrals and multiple singular integrals associated to certain lower-dimensional sets and the boundedness of multilinear singular integrals and commutators. It is consists of seven chapters as follows. In Chapter 1, we firstly give a brief review of the background of the related problems and state our main results. We...学位：理学博士院系专业：数学科学学院_基础数学学号：1902012015382

A Variant of Hormander's Condition and Weighted Estimates for Singular Integrals

设10和C_r>0,使对任意的y∈r~n和r>C_r|y|,有SuM((2kr)~(n/r')(InTEgrAl(︱k(X-y)-SuM(bJ(X)φJ(y)) frOM J=1 TO ∞︱_(dX)~r) frOM n=2krj(j = 1,...,m) are suitable functions.We say a kernel K satisfies a variant of the classical L~r-Hrmander's condition,if there exist constants c_r>0 and C_r>0,such that for any y∈R~n and R>c_r|y|, sum((2kR)~(n/r')(integral(︱K(x-y)-sum(Bj(x)φj(y)) from j=1 to ∞︱_(dx)~r) from n=2kR<︱x︱≤2(k+1)R))≤C_r In this paper,the authors establish the weighted norm inequalities for singular integral operators with kernel satisfying the above variant of the classical L~r-Hrmander's condition.国家自然科学基金资助项目(11041004); 黑龙江省自然科学基金项目(A200913

Estimates for Rough Singular Integrals Along Submanifolds of Finite Type on Product Domains via Extrapolation

本文致力于研究乘积空间上沿有限型的奇异积分算子,通过Fourier变换及外插方法的讨论,证明了带径向球面粗糙核的奇异积分算子的L~p(R~n×R~m)有界性.We consider the singular integrals associated with functions of finite type on product domains.By the delicate Fourier transform estimates and the extrapolation arguments,we obtain the L~p(R~n × R~m) boundedness for such operators with rough kernels both in the radial direction and on the spherical surface.Supported by NSFC(No.11171137);; the NSF of Zhejiang Province(No.LY12A01011

Commutators of Singular Integral Operators Satisfying a Variant of a Lipschitz Condition

Scientific Research Fund of Heilongjiang Provincial Education Department [12531720]Let T be a singular integral operator with its kernel satisfying vertical bar K(x - y) - Sigma(l)(k=1) B-k(x)phi(k)(y)vertical bar 2 vertical bar y vertical bar > 0, where B-k and phi(k) (k = 1,..., l) are appropriate functions and gamma and C are positive constants. For (b) over arrow = (b(1),...,b(m)) with b(j) is an element of BMO(R-n), the multilinear commutator T-(b) over arrow generated by T and (b) over arrow is formally defined by T((b) over arrow)f(x) = integral(n)(R) [Pi(m)(j=1) (b(j)(x) - b(j)(y))] K (x,y)f(y)dy In this paper, the weighted L-p-boundedness and the weighted weak type L logL estimate for the multilinear commutator T-(b) over bar are established

Parametric Marcinkiewicz Integrals with Rough Kernels Supported by Compound Subvarieties

研究沿复合曲线的粗糙核参数型MArCInkIEWICz积分算子,在积分核满足相当弱的尺寸条件下,建立了这些算子的l~P有界性.作为应用,相应于面积积分和lITTlEWOOd-PAlEy-g_λ~*函数的参数型MArCInkIEWICz积分算子的l~P有界性也被给出.In this paper,we establish the L~p boundedness for a class of rough parametric Marcinkiewicz integral operators associated with polynomial compound mappings,under rather weaker size conditions on the kernels,which essentially improve and generalize certain previous results.As applications,the L~p bounds of the corresponding parametric Marcinkiewicz integral operators related to area integrals and Littlewood-Paley g_λ~* functions are also obtained.国家自然科学基金(G11071200;11371295); 福建省自然科学基金(2010J01013)资

A note on rough singular integrals in Triebel-Lizorkin spaces and Besov spaces

NNSF of China [11071200]; NSF of Fujian Province of China [2010J01013]This paper is concerned with the singular integral operators along polynomial curves. The boundedness for such operators on Triebel-Lizorkin spaces and Besov spaces is established, provided the kernels satisfy rather weak size conditions both on the unit sphere and in the radial direction. Moreover, the corresponding results for the singular integrals associated to the compound curves formed by polynomial with certain smooth functions are also given

一种柔性磁性薄膜饱和磁致伸缩系数的测量方法

本发明提供了一种柔性磁性薄膜饱和磁致伸缩系数的测量方法。该方法采用由非磁性材料制成的、具有固定曲率半径的非磁性模具对柔性磁性薄膜产生应变，得到所施加应力与无应力存在时的应力差&Delta;&sigma;，然后利用磁光克尔效应测试系统测量该柔性磁性薄膜样品在无应变与应变条件下各向异性场的变化量&Delta;HK，通过饱和磁致伸缩系数公式&lambda;s=&Delta;HkMs/(3&Delta;&sigma;)，直接计算得到该柔性磁性薄膜的饱和磁致伸缩系数&lambda;s。与现有磁性薄膜的磁致伸缩系数测量方法相比，本发明具有测量精度高、简单易行、成本低的优点，具有良好的应用前景

江西药用植物新记录

报道产自武功山地区的7种江西省植物新记录,包括石松科Lycopodiaceae的昆明石杉Huperzia kunmingensis、虎耳草科Saxifragaceae的莽山绣球Hydrangea mangshanensis和腺鼠刺Iteaglutinosa、石竹科Lycopodiaceae的皱叶繁缕Stellaria monosperma var.japonica、菊科Compositae的川西黄鹌菜Youngiapratti,兰科Orchidaceae植物疏花虾脊兰Calanthehenryi和台湾吻兰Collabium formosanum。其中昆明石杉、莽山绣球、腺鼠刺、川西黄鹌菜和疏花虾脊兰5种为中国特有植物,疏花虾脊兰分布范围狭窄,ICUN将列为易危级别。该文对这些物种分布新区域的报道,扩宽其分布范围,丰富了江西省药用植物资源。凭证标本均保存于吉首大学植物标本馆(JIU)和中山大学标本室(SYS)