某些算子在局部紧的Vilenkin群上的Herz型Hardy空间

G表示局部紧的Vilenkin群， 在论文中作者将研究某些次线性算子和Calderón Zygmund算子在Herz型Hardy空间上的有界性.      

4-Dimensional Einstein Gravity Extended by a 3-Dimensional Gravitational Chern-Simons Term

When 4-dimensional general relativity is extended by a 3-dimensional gravitational Chern–Simons term an apparent violation of diffeormorphism invariance is extinguished by the dynamical equations of motion for the modified theory. The physical predictions of this recently proposed model show little evidence of symmetry breaking, but require the vanishing of the Pontryagin density.     

Some Hardy Type Inequalities in R~n

Some Hardy type inequalities on the ball and its complementary set in the Euclidean space are established by using the Picone type identity and constructing suitable auxiliary functions.     

The Poisson problem with mixed boundary conditions in Sobolev and Besov spaces in non-smooth domains

We introduce certain Sobolev-Besov spaces which are particularly well adapted for measuring the smoothness of data and solutions of mixed boundary value problems in Lipschitz domains. In particular, these are used to obtain sharp well-posedness results for the Poisson problem for the Laplacian with mixed boundary conditions on bounded Lipschitz domains which satisfy a suitable geometric condition introduced by R.Brown in (1994). In this context, we obtain results which generalize those by D.Jerison and C.Kenig (1995) as well as E.Fabes, O.Mendez and M.Mitrea (1998). Applications to Hodge theory and the regularity of Green operators are also presented.

     

半平面中解析函数的零点

对在半平面中属于加权Hardy空间,不恒为零且在某一固定点列上为零的解析函数的存在性给出了充分必要条件。     

具Hardy-Sobolev临界指数椭圆方程的非平凡解

运用精确估计和变分法得到具奇异位势的椭圆方程-△u-μu/|x|2=|u|2*(s)-2u/|x|s+λu,u∈H0(1,2)(Ω)的非平凡解的存在性,其中Ω是有光滑边界的有界开区域,μ,λ是两个正参数.     

Nash Inequalities for Markov Processes in Dimension One

In this paper, we give characterizations of Nash inequalities for birth-death process and diffusion process on the line. As a by-product, we prove that for these processes, transience implies that the semigroups P(t) decay as ∥P(t)∥_1→∞≥Ct ₋₁. Sufficient conditions for general Markov chains are also obtained. Received November 29, 2000, Revised February 21, 2001, Accepted March 16, 2001     

区域Hardy空间的原子分解和对偶空间

研究D-C chang等人引进的五个区域Hardy空间，刻划这些空间的原子分解和对偶空间，揭示了这些空间的内在联系。     

Boundedness of Sublinear Operators in Herz Spaces on Vilenkin Groups and its Application

The authors establish the boundedness of some sublinear operators in weighted Herz spaces on Vilenkin groups under certain weak local hypotheses on the size of these operators at the identity. This class of operators includes most of the important operators in harmonic analysis on Vilenkin groups. The main theorems are best possible under the conditions of the theorems. As applications, the authors establish the Littlewood-Paley function characterization of some Herz spaces and the relations between Herz spaces and Herz-type Hardy spaces.     

The effect of the counter-rotating terms on the Rabi oscillations and squeezing in the Dicke model with cavity losses

The effect of the counter-rotating terms in the Dicke model with cavity losses is examined. Numerical results for the time evolutions of the atomic population inversion, dipole moment, mean-photon number and atomic and field squeezing parameters for an initial coherent field are presented for various numbers of atoms and different cavity dampings. As a consequence of the counter-rotating terms, the appearance of new steady states for atomic population inversion and the mean-photon number is pointed out.