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.     

Large global solutions to 3-D inhomogeneous Navier-Stokes equations slowly varying in one variable

Motivated by Chemin and Gallagher (2010) [8], we consider the global wellposedness to the 3-D incompressible inhomogeneous Navier-Stokes equations with large initial velocity slowly varying in one space variable. In particular, we proved that when the initial density is close enough to a positive constant, then given divergence free initial velocity field of the type , as that in Chemin and Gallagher (2010) [8] for the classical Navier-Stokes system, we shall prove the global wellposedness of (INS) for ? sufficiently small. The main difficulty here lies in the fact that we will have to obtain the L¹(R⁺;Lip(R³)) estimate for convection velocity in the transport equation of (INS). Toward this and due to the strong anisotropic properties of the approximate solutions, we will have to work in the framework of anisotropic type Besov spaces here.     

具有非倍测度的Littlewood-Paley g_λ~*函数的多线性交换子的端点估计

令μ是R~d上可能为非倍的正的Radon测度.对于所有的x∈R~d,r>0以及某个固定的常数C_0,μ只需满足μ(B(x,r))≤C_0r~n(0相似文献   

Parameterized Littlewood-Paley operators and area integrals on weak hardy spaces

In this paper,we establish the boundedness of parameterized Littlewood-Paley operator μ*,ρλ and parameterized area integral μΩρ,S with kernel satisfying the logarithmic type Lipschitz condition on the weak Hardy space.     

Lipschitz estimates for multilinear commutator of Littlewood-Paley operator

In this paper, we will study the continuity of multilinear commutator generated by Littlewood-Paley operator and Lipschitz functions on Triebel-Lizorkin space, Hardy space and Herz-Hardy space.      

Littlewood Paley算子交换子在Herz型Hardy空间上的CBMO估计

考虑了Littlewood—Paley算子交换子的CBMO估计,利用原子分解得到了Littlewood—Paley算子与CBMO函数生成的交换子在Herz型Hardy空间上的有界性．     

Boundedness of the Littlewood—Paley Operator,the Function g（f）,on BMO（T）

Littlewood-Paley operator,the function g(f),is considered as an operator on BMO(T).It is proved that if f∈BMO(T),then g(f)∈BMO(T) and there is a constant C that is independent of f such that ||g(f)||*≤C||f||*.Moreover,we have got the further results.     

Littlewood-Paley算子的交换子的有界性

设n/(n+ε) 相似文献   

齐型空间上的Lipschitz函数与Littlewood－Paley g－函数

在θ阶正规齐型空间上，如果算子列｛Ｓｋ｝ｋ∈Ｚ是恒等逼近，Ｄｋ＝Ｓｋ－Ｓｋ－１；本文给出一个用｛Ｄｋ｝ｋ∈Ｚ表达的ｆ∈Ｌｉｐα（Ｌｉｐｓｃｈｉｔｚ函数类，０＜α＜θ）的充分必要条件．作为其推论得到，对于ｆ∈ＬＩｐα，其Ｌｉｔｔｌｅｗｏｏｄ－Ｐａｌｅｙｇ函数ｇ（ｆ）（Ｘ）或者处处为无穷大，或者在Ｌｉｐα上有界．     

Analytic wavelets generated by radial functions

In this paper, we deal with a class of non-stationary multiresolution analysis and wavelets generated by certain radial basis functions. These radial basis functions are noted for their effectiveness in terms of projection, such as interpolation and least-squares approximation, particularly when the data structure is scattered or the dimension of ^s is large. Thus projecting a functionf onto a suitable multiresolution space is relatively easy here. The associated multiresolution spaces approximate sufficiently smooth functions exponentially fast. The non-stationary wavelets satisfy the Littlewood-Paley identity so that perfect reconstruction of wavelet decompositions is achieved. For the univariate case, we give a detailed analysis of the time-frequency localization of these wavelets. Two numerical examples for the detection of singularities with analytic wavelets are provided.Supported by NSF Grant #DMS-92-06928, Air Force Grant #F49620-92-J-0403DEF and NATO Grant #CR-900158.