Lizhong Peng

Lp boundedness of commutators of Riesz transforms associated to Schrödinger operator

Abstract In this paper we consider L p boundedness of some commutators of Riesz transforms associated to Schrodinger operator P = − Δ + V ( x ) on R n , n ⩾ 3 . We assume that V ( x ) is non-zero, non-negative, and belongs to B q for some q ⩾ n / 2 . Let T 1 = ( − Δ + V ) −1 V , T 2 = ( − Δ + V ) − 1 / 2 V 1 / 2 and T 3 = ( − Δ + V ) − 1 / 2 ∇ . We obtain that [ b , T j ] ( j = 1 , 2 , 3 ) are bounded operators on L p ( R n ) when p ranges in a interval, where b ∈ BMO ( R n ) . Note that the kernel of T j ( j = 1 , 2 , 3 ) has no smoothness.

The Laurent series on the octonions

In this paper, we obtained the Laurent series theorem on the octonions.

Characterization of octonionic analytic functions

It is shown that there is only one possible way to define the O-analytic functions. A simple way to construct the O-analytic functions is also given.

Admissible Wavelets on the Siegel Domain of Type One

LetSp(n, R) be the sympletic group, and letKn* be its maximal compact subgroup. ThenG=Sp(n,R)/Kn* can be realized as the Siegel domain of type one. The square-integrable representation ofG gives the admissible wavelets AW and wavelet transform. The characterization of admissibility condition in terms of the Fourier transform is given. The Bergman kernel follows from the viewpoint of coherent state. With the Laguerre polynomials, Hermite polynomials and Jacobi polynomials, two kinds of orthogonal bases for AW are given, and they then give orthogonal decompositions ofL2-space on the Siegel domain of type one ℒ(ℋn, |y| *dxdy).

Background modeling for dynamic scenes using tensor decomposition

Background modeling is an important topic in video analysis and understanding, while the main difficulty lies in the dynamic scenes. The scenes with limited variation can be effectively described by numerous models, but more precise representation model are needed for complex scenes. In this paper, we propose a background modeling algorithm for dynamic scenes using tensor decomposition. Since video data can be naturally represent as higher-order tensors, the tensor methods can accurately describe the dynamic nature of the nearby pixels, and then background will be estimated by the low-rank representation of tensors. Experimental results show that the proposed method is robust and adaptive in dynamic environments, and furthermore, moving objects can be clearly separated from the complex dynamic background.