Loeb空间上一类右连续过程最优停止的非标准表示

本文在Loeb空间上得到了右连续左半上连续的随机过程的SRC提升．证明了一个内过程的S-最优停止的存在性,并得到了它的结构性表示．最后证明了一个过程SRC提升的S-最优停止的标准部分即为对应标准过程的最优停止,在Loeb空间上推广了[8]中的结果．     

Radon概率空间中随机过程到Loeb概率空间中的转换

在Lindstrom于1980年工作的基础上进一步研究了标准概率空间的弱Loeb空间表示的性质，把Radon概率空间中的局部鞅和半鞅转换到了超有限的Loeb概率空间中，为非标准分析方法在随机分析中的应用提供了一个有效的框架。     

关于σ-有限测度空间的Loeb空间的一点注记

以一种自然的方式定义了σ－有限测度空间的Loeb空间，并研究了其若干性质，将有限Loeb测定空间的一些重要性质推广到σ－有限情形，并将Loeb测度对有限Radon测度的刻画定理推广到σ－有限情形。     

Loeb空间上一类右连续过程最优停止的非标准表示

本文在Loeb空间上得到了右连续左半上连续的随机过程的SRC提升．证明了一个内过程的S-最优停止的存在性,并得到了它的结构性表示．最后证明了一个过程SRC提升的S-最优停止的标准部分即为对应标准过程的最优停止,在Loeb空间上推广了[8]中的结果．     

算子空间的原子性

研究了算子空间的原子性.证明了算子空间V是原子当且仅当V是正合且有限内射; V内的任意一个有限维算子子空间是原子当且仅当V是原子且V内任意有限维算子子空间足V的完全补.因此作为推论,得到了无限维箅子空间V的任意有限维子空间是原子,则V是1-Hilbertian和1-齐次.     

算子空间的原子性

研究了算子空间的原子性.证明了算子空间V是原子当且仅当V是正合且有限内射; V内的任意一个有限维算子子空间是原子当且仅当V是原子且V内任意有限维算子子空间足V的完全补.因此作为推论,得到了无限维箅子空间V的任意有限维子空间是原子,则V是1-Hilbertian和1-齐次.     

Lebesgue-Bochner函数空间的对偶表示定理 *

利用随机共轭空间的表示定理证明了一个一般的对偶表示定理 .作为应用 ,统一并改进了关于Lebesgue Bochner函数空间的对偶表示方面许多熟知的重要定理     

关于L2(Rd)中仿射子空间小波标架的一个注记

研究了L2(Rd)的有限生成仿射子空间中小波标架的构造.证明了任意有限生成仿射子空间都容许一个具有有限多个生成元的Parseval小波标架,并且得到了仿射子空间是约化子空间的一个充分条件.对其傅里叶变换是一个特征函数的单个函数生成的仿射子空间,得到了与小波标架构造相关的投影算子在傅里叶域上的明确表达式,同时也给出了一些例子.     

完备格中的成分理论

在完备格中引入了元素的成分概念．基于此,引入了元素的宽度的概念．在分配格的情形证明了元素的成分集对有限并运算封闭且有某种遗传性．证明了元素的有限宽度的成分之集是定向集．称没有非平凡成分的元素为颗粒．称每个非零元素都可表示为其颗粒成分之并的完备格为颗粒表示格．证明了拓扑空间是局部连通的充要条件是其开集格为颗粒表示格．     

Lomonosov引理的逆命题成立

证明了著名的Lomonosov引理的逆命题成立,得到了(?)(X)的一个子代数有 非平凡的不变闭子空间的充要条件.这里(?)(X)表示Banach空间X上的有界线性算 子全体所成的Banach代数.     

Boundedness of Riesz Potentials in Nonhomogeneous Spaces

For a class of linear operators including Riesz potentials on R^d with a nonnegative Radon measure μ, which only satisfies some growth condition, the authors prove that their boundedness in Lebesgue spaces is equivalent to their boundedness in the Hardy space or certain weak type endpoint estimates, respectively. As an application, the authors obtain several new end estimates.     

Boundedness of Commutators with Lipschitz Functions in Non-homogeneous Spaces

Under the assumption that the underlying measure is a non-negative Radon measure which only satisfies some growth condition, the authors prove that for a class of commutators with Lipschitz functions which include commutators generated by Calderon-Zygmund operators and Lipschitz functions as examples, their boundedness in Lebesgue spaces or the Hardy space H1 (μ) is equivalent to some endpoint estimates satisfied by them. This result is new even when the underlying measureμis the d-dimensional Lebesgue measure.     

Existence for a degenerate Cauchy problem

We prove the existence of a solution to the degenerate parabolic Cauchy problem with a possibly unbounded Radon measure as an initial data. To accomplish this, we establish a priori estimates and derive a compactness result. We also show that the result is optimal in the Euclidian setting.     

Semi-classical propagation of singularities for the Stokes system

Abstract

We study the quasi-mode of Stokes system posed on a smooth bounded domain Ω with Dirichlet boundary condition. We prove that the semi-classical defect measure associated with a sequence of solutions concentrates on the bicharacteristics of Laplacian as a matrix-valued Radon measure. Moreover, we show that the support of the measure is invariant under the Melrose-Sjöstrand flow.     

EXISTENCE AND UNIQUENESS OF ENTROPY SOLUTION TO PRESSURELESS EULER SYSTEM WITH A FLOCKING DISSIPATION

We study the existence and uniqueness problem for the nonhomogeneous pressureless Euler system with the initial density being a Radon measure. Our uniqueness result is obtained in the same space as the existence theorem. Besides, by counterexample we prove that Huang-Wang's energy condition is also necessary for our nonhomogeneous system.     

Product of functions in BMO and <Emphasis Type="Italic">H</Emphasis><Superscript>1</Superscript> in non-homogeneous spaces

Under the assumption that the underlying measure is a non-negative Radon measure which only satisfies some growth condition and may not be doubling, we define the product of functions in the regular BMO and the atomic block H ¹ in the sense of distribution, and show that this product may be split into two parts, one in L ¹ and the other in some Hardy-Orlicz space.     

A Radon–Nikodym type theorem for forms

The Lebesgue decomposition theorem and the Radon–Nikodym theorem are the cornerstones of the classical measure theory. These theorems were generalized in several settings and several ways. Hassi, Sebestyén, and de Snoo recently proved a Lebesgue type decomposition theorem for nonnegative sesquilinear forms defined on complex linear spaces. The main purpose of this paper is to formulate and prove also a Radon–Nikodym type result in this setting. As an application, we present a Lebesgue type decomposition theorem and solve a special case of the infimum problem for densely defined (not necessarily bounded) positive operators.     

HARNACK''S INEQUALITY FOR GENERALIZED SUBELLIPTIC SCHR(O)DINGER OPERATORS

We prove a uniform Hamack inequality for nonnegative solutions of △Gu- μμ=0, where △G is a sublaplacian, μ is a non-negative Radon measure and satisfying scale-invariant Kato condition.     

Anisotropic Parabolic Equations with Measure Data

In this paper, we prove the existence of solutions to anisotropic parabolic equations with right hand side term in the bounded Radon measure M(Q) and the initial condition in M(Ω) or in L^m space (with m “small”).