带粗糙核的奇异积分交换子的有界性

本文研究了带粗糙核的奇异积分算子与BMO函数生成的交换子的有界性问题.利用原子分解的方法,获得了带粗糙核的奇异积分交换子TΩb在Lp空间、Hardy空间、弱Hardy空间上的有界性结果,推广了交换子Tb在各类函数空间上有界性的结果.     

沿有限型的粗糙核奇异积分算子在乘积空间上的外插估计（英文）

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.     

加权Herz空间上交换子的有界性

旨在建立一大类由BMO函数和线性算子所生成交换了在另权Herz空间上的有界性,这些线性算子包括Calderon-Zygmund奇异积分算子,带有粗糙核的R.Fefferman型奇积分算子和带有粗糙核的Ricci-Stein-振荡奇异积分算子。     

齐次Morrey-Herz空间中交换子的中心BMO估计

设T_b为广义Hardy算子和中心BMO函数生成的交换子,本文得到了该交换子在齐次加权Morrey-Herz空间中的有界性.而且,本文给出了带粗糙核的多线形奇异积分算子在齐次Morrey-Herz空间中的中心BMO估计.     

多线性振荡积分的一个注记

本文研究了有关粗糙核的多线性振荡奇异积分算子,给出了这类算子有界性的判定准则．     

奇异积分算子在乘积Triebel—Lizorkin空间

本文讨论了一类粗糙的奇异积分算子在乘积Triebel—Lizorkin空间中的有界性,以及分数次积分算子和Littlewood—Paley函数在此空间的有界性,改进和推广了以前的结果．     

多线性分数次奇异积分在弱 Hardy 空间的Lipschitz 估计

讨论了一类具有粗糙核多线性分数次奇异积分算子在弱 Hardy 空间的性质,通过原子分解,得到了这类算子在弱Hardy空间的有界性.     

沿超曲面的强奇异积分算子在调幅空间上的有界性

设■该文主要讨论了上述奇异积分算子在广义的调幅空间上的有界性,其中粗糙核Ω∈L~1(S~(n-2))h(y)为有界的径向函数,而γ(y)是满足一定条件的超曲面.     

无界集上带粗糙核的分数次积分算子及其交换子在消失广义变指标Morrey空间的有界性（英文）

本文研究了无界集上带粗糙核的分数次积分算子及其交换子在消失广义变指标Morrey的空间有界性.利用变指标函数的性质和算子T?,α及其交换子[b, T?,α]在变指标Lebesgue空间的逐点估计,获得了无界集上带粗糙核的分数次积分算子T?,α及其交换子[b, T?,α]在消失广义变指标Morrey空间的有界性,推广了已有的结果.     

沿旋转曲面奇异积分的有界性

本文建立了具有粗糙核的沿曲面奇异积分算子的L^P有界性．其中粗糙核K(y)=Ω（y)/|y|^n,y∈R^n以及曲面{(y，φ(|y|）)：y∈R^n)满足某种光滑条件．同时，相应极大算子的有界性也被得到.     

Strongly Singular Calderon-Zygmund Operator and Commutator on Morrey Type Spaces

In this paper, the author considers the boundedness of strongly singular Calderdn Zygmund operator and commutator generated by this operator and Lipschitz function on the classical Morrey space and generalized Morrey space. Moreover, the boundedness of strongly singular Calderón- Zygmund operator on the predual of Morrey space is discussed.     

板几何中一类具反射边界条件的奇异迁移算子的谱

在L^p（1〈P〈∞）空间上研究板几何中一类具反射边界条件下各向异性、连续能量、均匀介质的奇异迁移方程．证明其奇异迁移算子产生C0半群和该半群的Dyson-Phillips展开式的二阶余项是紧的,且得到了该算子的谱在区域Г中由具有限代数重数的离散本征值组成等结果．     

强奇异积分算子交换子的端点估计

本文考虑强奇异积分算子的交换子在Hardy型空间上的端点估计,建立了这类交换子从H¹（Rⁿ）到弱 L¹（Rⁿ）上的有界性及H¹（Rⁿ）的某个子空间到 L¹（Rⁿ）上的有界性结果.     

Almost-Normed Spaces of Functions with Given Asymptotics, Lagrangian Asymptotics, and Their Application to Ordinary Differential Equations

The concept of almost-normed spaces is introduced. It is proved that the space of sufficiently smooth functions asymptotically approximating to polynomials (of degrees no higher than a given one) as their argument tends to infinity is an almost-normed space. It is demonstrated that this space is a complete metric space with respect to the metrics generated by the almost-norm introduced. The space of functions strongly asymptotically approximating to polynomials is defined, and its embedding into the space of functions asymptotically approximating to polynomials is proved. The results obtained give a new approach to studying boundary-value problems with asymptotic initial value data at singular points of ordinary differential equations.     

Cavitation and Singular Solutions in Nonlinear Elastodynamics

Based on works of Ball (1982) and Pericak-Spector and Spector (1988), we investigate singular solutions to the compressible nonlinear elastodynamics equations. These solutions have discontinuous displacement fields and describe fracture or cavitation. We explore a definition of singular solution via approximating sequences of smooth functions. We employ these approximating sequences to investigate the energy of such solutions, taking into account the energy needed to open a crack or hole. We show that the existence of singular solutions and the finiteness of their energy is strongly related to the behavior of the stress response function for infinite stretching. We outline our findings in one space dimension. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A note on the Bogomolov-type smoothness on deformations of the regular parts of isolated singularities

We apply the Tian-Todorov method, proving the Bogomolov
smoothness theorem (for deformations of compact Kähler manifolds) to deformations of the regular part of a Stein space with a finite number of isolated singular points. By the argument based on the Hodge structure on a strongly pseudo-convex Kähler domain or on a punctured Kähler space, we obtain an unobstructed subspace of the infinitesimal deformation space.

     

强奇异Calder-Zygmund积分及其交换子在 Hardy 型空间上的有界性

给出了局部 Hardy 空间 $h^{p}(\mathbb{R}^{n})$\ $\big(\frac{n}{n+1}相似文献   

Boundedness of Commutators on Hardy-Type Spaces

In this paper, the boundedness of the commutator generated by strongly singular Calderón-Zygmund operator and a Lipschitz function is discussed on the classical Hardy spaces and the Herz-type Hardy spaces. The authors also get the boundedness of the strongly singular Calderón-Zygmund operator itself and the commutator generated by strongly singular Calderón-Zygmund operator and a BMO function on the Herz-type Hardy spaces.     

板几何中一类具周期边界条件的奇异迁移算子的谱

在Lp(1相似文献   

Three Dimensional Interface Problems for Elliptic Equations

The author studies the structure of solutions to the interface problems for second order linear elliptic partial differential equations in three space dimension.The set of singular points consists of some singular lines and some isolated singular points.It is proved that near a singular line or a singular point,each weak solution can be decomposed into two parts,a singular part and a regular part.The singular parts are some finite sum of particular solutions to some simpler equations,and the regular parts are bounded in some norms,which are slightly weaker than that in the Sobolev space H~2.