Lp BOUNDEDNESS OF COMMUTATOR OPERATOR ASSOCIATED WITH SCHROEDINGER OPERATORS ON HEISENBERG GROUP

Let L=△Hn + V be a Schrdinger operator on Heisenberg group H n,where △Hn is the sublaplacian and the nonnegative potential V belongs to the reverse H¨older class BQ/2,where Q is the homogeneous dimension of H n.Let T1 =(△Hn + V)-1 V,T2 =(△Hn +V)-1/2 V 1/2,and T 3 =(△Hn +V)-1/2 Hn,then we verify that [b,Ti],i = 1,2,3 are bounded on some Lp(Hn),where b ∈ BMO(Hn).Note that the kernel of Ti,i=1,2,3 has no smoothness.     

L boundedness of commutator operator associated with schrödinger operators on heisenberg group

Let L = −ΔHⁿ + V be a Schrödinger operator on Heisenberg group Hⁿ, where ΔHⁿ is the sublaplacian and the nonnegative potential V belongs to the reverse Hölder class B_Q/2, where Q is the homogeneous dimension of Hⁿ  . Let T₁=(−ΔHn+V)⁻¹V,T₂=(−ΔHn+V)^−1/V₂1/2$T_1={(-\Delta H^n+V)}^{-1}V,T_2={(-\Delta H^n+V)}^{-1/2_{V}1/2}$, and T₃=(−Δ_Hn+V)^−1/2_∇Hn$T_3={(-{\Delta }_{H^n}+V)}^{-1/2}{\nabla }_{H^n}$, then we verify that [b, T_i], i = 1,2,3 are bounded on some L^p(Hⁿ), where b ∈ BMO(Hⁿ). Note that the kernel of T_i, i = 1,2,3 has no smoothness.     

由Campanato型函数和与薛定谔算子相关的Riesz变换生成的Toeplitz算子的有界性

本文研究了由Campanato型函数及与Schrödinger算子相关的Riesz变换生成的Toeplitz算子的有界性.利用Sharp极大函数估计得到了Toeplitz算子Θ^b在Lebesgue空间的有界性,拓广了已有交换子的结果.     

LITTLEWOOD-PALEY THEOREM FOR SCHR(O)DINGER OPERATORS

Let H be a Schr(o)dinger operator on Rn. Under a polynomial decay condition for the kernel of its spectral operator, we show that the Besov spaces and Triebel-Lizorkin spaces associated with H are well defined. We further give a Littlewood-Paley characterization of Lp spaces in terms of dyadic functions of H. This generalizes and strengthens the previous result when the heat kernel of H satisfies certain upper Gaussian bound.     

AREA FUNCTIONS ON HARDY SPACES ASSOCIATED TO SCHR(O)DINGER OPERATORS

In this paper, the author gives a characterization of atomic Hardy spacesassociated to Schrodinger operators by using area functions, and hence gets the dual spacesof atomic Hardy spaces.     

ISOMORPHISMS OF VARIABLE HARDY SPACES ASSOCIATED WITH SCHRÖDINGER OPERATORS

Let L:=-△+V be the Schrodinger operator on Rⁿwith n≥3,where V is a non-negative potential satisfying△^-1(V)∈L^∞(Rⁿ).Let w be an L-harmonic function,determined by V,satisfying that there exists a positive constantδsuch that,for any x∈Rn,0<δ≤w(x)≤1.Assume that p(·):Rⁿ→(0,1]is a variable exponent satisfying the globally log-H?lder continuous condition.In this article,the authors show that the mappings HL^p(·))(Rⁿ)■f■wf∈H^p(·)(Rⁿ)and HL^p(·)(Rⁿ)■f■(-△)^1/2L^-1/2(f)∈H^p(·)(Rⁿ)are isomorphisms between the variable Hardy spaces HL^p(·)(Rⁿ),associated with L,and the variable Hardy spaces H^p(·)(Rⁿ).     

A WEIGHTED ESTIMATE OF THE HORMANDER MULTIPLIER ON THE HEISENBERG GROUP

In this article, the authors prove the weighted boundedness of Hormander-type multiplier on the Heisenberg group.     

Schr(o)der函数的值分布

本文研究了Schr(o)der方程亚纯解的值分布.应用Ahlfors覆盖曲面理论,证明了任意从原点出发的射线都是Schr(o)der函数的Ahlfors方向;同时证明了这些射线还是Schr(o)der函数的T方向和Borel方向.     

TIME DECAY FOR SCHR(O)DINGER EQUATION WITH ROUGH POTENTIALS

We obtain certain time decay and regularity estimates for 3D Schrodinger equation with a potential in the Kato class by using Besov spaces associated with Schrodinger operators.     

Some properties of Riesz potential associated with Schr(O)dinger operator

Let (L) =-△ + V be the Schr(o)dinger operator on Rd,d ≥ 3,where △ is the Laplacian on Rd and V （≠） 0 is a nonnegative function satisfying the reverse H(O)lder inequality.In this article,the author inve...     

具相互作用项的非线性Schr(o)dinger方程的散射

In this paper,we give a simplified proof on the energy scattering for the nonlinear Schr(o)dinger equations with interaction terems by u8e of the interaction Morawetz estimate,which is originally introduced in[4].     

广义的带导数非线性薛定谔方程的有理解

广义带导数非线性薛定谔方程是与Kaup-Newell谱问题相联系的一个非线性发展方程,方程可在合适的条件方程下,利用Wronsiki技巧,寻找广义双Wronsikian形式的一般解,进而得到其孤子解和有理解.     

无界区域R3上的非线性应变波方程与薛定谔方程藕合方程组的指数吸引子

本文研究了无界区域R~3上的非线性应变波方程与薛定谔方程藕合方程组.运用带权空间构造一类紧算子和算子分解的方法,得到了该方程在无界区域R3上的H~2×H~2×H~1(R~3)中拥有一个指数吸引子.     

Spectral analysis of nonselfadjoint Schr(o)dinger problem with eigenparameter in the boundary condition

In this paper we consider the nonselfadjoint (dissipative) Schr(o)dinger boundary value problem in the limit-circle case with an eigenparameter in the boundary condition. Since the boundary conditions are nonselfadjoint, the approach is based on the use of the maximal dissipative operator,and the spectral analysis of this operator is adequate for the boundary value problem. We construct a selfadjoint dilation of the maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We construct a functional model of the maximal dissipative operator and define its characteristic function in terms of solutions of the corresponding Schr(o)dinger equation. Theorems on the completeness of the system of eigenvectors and the associated vectors of the maximal dissipative operator and the Schr(o)dinger boundary value problem are given.