Singular Hartree equation in fractional perturbed Sobolev spaces

We establish the local and global theory for the Cauchy problem of the singular Hartree equation in three dimensions, that is, the modification of the non-linear Schrödinger equation with Hartree non-linearity, where the linear part is now given by the Hamiltonian of point interaction. The latter is a singular, self-adjoint perturbation of the free Laplacian, modelling a contact interaction at a fixed point. The resulting non-linear equation is the typical effective equation for the dynamics of condensed Bose gases with fixed point-like impurities. We control the local solution theory in the perturbed Sobolev spaces of fractional order between the mass space and the operator domain. We then control the global solution theory both in the mass and in the energy space.     

Boundedness of Commutators Generated by Campanato-type Functions and Riesz Transforms Associated with Schrdinger Operators

Let■=-△+V be a Schrdinger operator on R~n,n3,where △is the Laplacian on R~n and V≠0 is a nonnegative function satisfying the reverse Holder's inequality.Let[b,T]be the commutator generated by the Campanatotype function b∈■ and the Riesz transform associated with Schrdinger operator T=▽(-△+V)~(-1/2).In the paper,we establish the boundedness of[b,T]on Lebesgue spaces and Campanato-type spaces.     

Maximal operators of commutators of Bochner-Riesz means with Lipschitz functions

This paper presents a weighted L ² estimate with power weights for the maximal operator of commutators generated by compactly supported multipliers and Lipschitz functions. As an application, we study the almost convergence of the commutators, which is generated by the Bochner-Riesz means under the critical index and Lipschitz functions, for functions in L ^p (p ⩾ 2).     

Bochner-Riesz的极大交换子的几个端点估计

建立了极大Bochner-Riesz算子的极大交换子的（Ln/β,BMO）和（Lp,Lipβ-n/p）有界性.     

θ型Calderón-Zygmund算子交换子的CBMO估计

讨论了满足一定条件的θ型Calderon—Zygmund奇异积分与CBMO函数生成的交换子在HAb^p空间及Herz型Hardy空间上的有界性．     

An algorithm and its application for obtaining some kind of infinite-dimensional Hamiltonian canonical formulation

Using factorization viewpoint of differential operator, this paper discusses how to transform a nonlinear evolution equation to infinite-dimensional Hamiltonian linear canonical formulation. It proves a sufficient condition of canonical factorization of operator, and provides a kind of mechanical algebraic method to achieve canonical evolution equation, infinite-dimensional Hamiltonian canonical system, factorization of differential operator, commutator,evolution equation, infinite-dimensional Hamiltonian canonical system, factorization of differential operator, commutatorProject supported by the National Natural Science Foundation of China (Grant No~10562002) and the Natural Science Foundation of Nei Mongol, China (Grant No~200508010103).2007-05-09{\partial}/{\partial x}Corresponding author．E-mail：alatanca@imu．edu.cn/qk/85823A/200711/25754042.html0200, 03405/9/2007 12:00:00 AMUsing factorization viewpoint of differential operator, this paper discusses how to transform a nonlinear evolution equation to infinite-dimensional Hamiltonian linear canonical formulation. It proves a sufficient condition of canonical factorization of operator, and provides a kind of mechanical algebraic method to achieve canonical $`{\partial}/{\partial x}'$-type expression, correspondingly. Then three examples are given, which show the application of the obtained algorithm. Thus a novel idea for inverse problem can be derived feasibly.http://cpb.iphy.ac.cn/CN/10.1088/1009-1963/16/11/002https://cpb.iphy.ac.cn/CN/article/downloadArticleFile.do?attachType=PDF&id=1088382007-11-20'-type expression, correspondingly. Then three examples are given, which show the application of the obtained algorithm. Thus a novel idea for inverse problem can be derived feasibly.     

调和Bergman空间上Toeplitz算子的代数性质

In this paper, we first investigate the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols on the harmonic Bergman space. Next, we characterize finite rank commutators and semi-commutators of two Toeplitz operators with quasihomogeneous symbols.     

抽象Heisenberg不等式中的交换子

在抽象的Ｈｅｉｓｅｎｂｅｒｇ不等式中,交换于「Ａ,Ｂ」可能不是闭的或其定义也许太小,通过改变「Ａ,Ｂ」的定义及某种弱下的形式,对某一类自共轭算子给出了一个充分条件,使在该条件下「Ａ,Ｂ」的作用可用一个自共轭算代替,与比较,该条件更容易验证。     

单边奇异积分交换子的加权变差不等式

本文主要研究了单边Calder\''{o}n-Zygmund奇异积分交换子的加权变差不等式,即建立了单边Calder\''{o}n-Zygmund奇异积分与Lipschitz函数生成的交换子的加权变差不等式, 同时,利用权的外推法得到了该交换子在Triebel-Lizorkin空间上的加权变差不等式.