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．     

On the Carey–Helton–Howe–Pincus trace formula

In this article, we give a new proof of the Carey–Helton–Howe–Pincus trace formula using Kato's theory of “relatively-smooth” operators and Krein's trace formula.     

On the sum of a narrow and a compact operators

Our main technical tool is a principally new property of compact narrow operators which works for a domain space without an absolutely continuous norm. It is proved that for every Köthe F-space X and for every locally convex F-space Y   the sum _T1+_T2$T_1+T_2$ of a narrow operator _T1:X→Y$T_1:X\to Y$ and a compact narrow operator _T2:X→Y$T_2:X\to Y$ is a narrow operator. This gives a positive answers to questions asked by M. Popov and B. Randrianantoanina [6, Problems 5.6 and 11.63].     

On Gauge Invariant Regularization of Fermion Currents

We compare Schwinger and complex powers methods to construct regularized fermion currents. We show that, although both of them are gauge invariant, they are not always yield the same result.     

Regularization method with two parameters for nonlinear ill-posed problems

This paper is devoted to the regularization of a class of nonlinear ill-posed problems in Banach spaces. The operators involved are multi-valued and the data are assumed to be known approximately. Under the assumption that the original problem is solvable, a strongly convergent approximation procedure is designed by means of the Tikhonov regularization method with two pa- rameters.     

Threshold properties of matrix-valued Schrödinger operators, II. Resonances

We present some results on the perturbation of eigenvalues embedded at a threshold for a matrix-valued Hamiltonian with three-dimensional dilation analytic Schrödinger operators as entries and with a small off-diagonal perturbation. The main result describes how a threshold eigenvalue generates resonances (that is, poles of the meromorphic continuation of the perturbed Hamiltonian).     

Approximation properties of modified Gamma operators

In this paper we present a survey of rates of pointwise approximation of modified Gamma operators Gn for locally bounded functions and absolutely continuous functions by using some inequalities and results of probability theory with the method of Bojanic-Cheng. In the paper a kind of locally bounded functions is introduced with different growth conditions in the fields of both ends of interval (0,+∞), and it is found out that the operators have different properties compared to the Gamma operators discussed in [X.M. Zeng, Approximation properties of Gamma operators, J. Math. Anal. Appl. 311 (2005) 389-401]. And we obtain two main theorems. Theorem 1 gives an estimate for locally bounded functions which subsumes the approximation of functions of bounded variation as a special case. Theorem 2 gives an estimate for absolutely continuous functions which is best possible in the asymptotical sense.     

Representation of Fourier Integral Operators Using Shearlets

Traditional methods of time-frequency and multiscale analysis, such as wavelets and Gabor frames, have been successfully employed for representing most classes of pseudodifferential operators. However, these methods are not equally effective in dealing with Fourier Integral Operators in general. In this article, we show that the shearlets, recently introduced by the authors and their collaborators, provide very efficient representations for a large class of Fourier Integral Operators. The shearlets are an affine-like system of well-localized waveforms at various scales, locations and orientations, which are particularly efficient in representing anisotropic functions. Using this approach, we prove that the matrix representation of a Fourier Integral Operator with respect to a Parseval frame of shearlets is sparse and well-organized. This fact recovers a similar result recently obtained by Candès and Demanet using curvelets, which illustrates the benefits of directional multiscale representations (such as curvelets and shearlets) in the study of those functions and operators where traditional multiscale methods are unable to provide the appropriate geometric analysis in the phase space. The second author was supported in part by a National Science Foundation grant DMS 0604561.