ROUGH OPERATORS AND COMMUTATORS ON HOMOGENEOUS WEIGHTED HERZ SPACES

The authors establish the baundedness on homogeneous weighted Herz spaces for a large class of rough operators and their commutators with BMO functions. In particular, the Calderon-Zygmund singular integrals and the rough R. Fefferman singular integral operators and the rough Ricci-Stein oscillatory singular integrals and the corresponding commutators are considered.

重复齐次化问题的强收敛率

In this paper,we study the reiterated homogenization operators Lε=-div(A(x/ε,x/ε^(2))∇).We establish the homogenized problem and representation equa-tion by introducing the two correctors.As a consequence,we obtain the H10 and L2 convergence estimates of solutions.

Existence and Uniqueness of Positive Periodic Solutions for First-order Functional Differential Equations

In this paper, we prove the existence and uniqueness of positive periodic solutions for first-order functional differential equation y＇（t） = α（t）y（t） ＋ f（t, y（t -τ-（t））） ＋ g（t）by using two fixed point theorems of general α-concave operators and homogeneous operators in ordered Banach spaces.

Compactness of the commutators of homogeneous singular integral operators

Let TΩ be the singular integral operator with kernel Ω（x）/｜x｜n where is homogeneous of degree zero, integrable and has mean value zero on the unit sphere Sn-1. In this paper, by Fourier transform estimates, Littlewood-Paley theory and approximation, the authors prove that if Ω∈（lnL）2 （Sn- 1）, then the commutator generated by TΩ and CMO（Rn） function, and the corresponding discrete maximal operator, are compact on LP（Rn, ｜s｜γp） for p∈ （1, ∞） and γp ∈ （-1, p-l）

A NOTE OF THE SPECTRUM OF HOMOGENEOUS COMPACT OPERATORS

In this paper, we present some counterexamples which show that there is no theory on the spectrum of homogeneous compact operators which parallels the Riesz-Schauder theory on the spectrum of linear compact operators. These counterexamples also illustrate that it is impossible to study in a unified setting the Fucik spectrum of the Laplacian: -△w = au+ - bu- inΩand u = 0 on (?)Ω, as well as the spectrum of the p-Laplacian: -div(|(?)u| p-2(?)u) = λ|u|p-2u and u = 0 on (?)Ω.

Euler Operator and Homogeneous Hida Distributions

Let（S）L2（S’（IR）,μ）（S）* be the Gel’fand triple over the white noise space （S’（IR）,μ）.Let（en,n≥0）be the ONB of L2（IR）consisting of the eigenfunctions of the s.a. operator-（d/（dt））2+1+t2.In this paper the Euler operator △E is defined as the sum ∑i【,ei)i, where i stands for the differential operator Dei.It is shown that △E is the infinitesimal gen- erator of the semigroup（Tt）,where(Tt)（x）=（etx）for ∈（S）.Similarly to the finite dimensional case,the λ-order homogeneous test functionals are characterized by the Euler equa- tion:△E=λ.Via this characterization the λ-order homogeneous Hida distributions are defined and their properties are worked out.

METRIC GENERALIZED INVERSE OF LINEAR OPERATOR IN BANACH SPACE

The Moore-Penrose metric generalized inverse T+ of linear operator T in Banach space is systematically investigated in this paper. Unlike the case in Hilbert space, even T is a linear operator in Banach Space, the Moore-Penrose metric generalized inverse T+ is usually homogeneous and nonlinear in general. By means of the methods of geometry of Banach Space, the necessary and sufficient conditions for existence, continuitv, linearity and minimum property of the Moore-Penrose metric generalized inverse T+ will be given, and some properties of T+ will be investigated in this paper.