NON-CONFLICTING ORDERING CONES AND VECTOR OPTIMIZATION IN INDUCTIVE LIMITS

Let(E, ξ) = ind(En, ξn) be an inductive limit of a sequence(En, ξn)n∈N of locally convex spaces and let every step(En, ξn) be endowed with a partial order by a pointed convex(solid) cone Sn. In the framework of inductive limits of partially ordered locally convex spaces,the notions of lastingly efficient points, lastingly weakly efficient points and lastingly globally properly efficient points are introduced. For several ordering cones, the notion of non-conflict is introduced. Under the requirement that the sequence(Sn)n∈N of ordering cones is nonconflicting, an existence theorem on lastingly weakly efficient points is presented. From this,an existence theorem on lastingly globally properly efficient points is deduced.     

Endpoint estimates for multilinear fractional integrals with non-doubling measures

Under the assumption that μ is a non-doubling measure on Rdwhich only satisfies the polynomial growth condition,the authors obtain the boundedness of the multilinear fractional integrals on Morrey spaces,weak-Morrey spaces and Lipschitz spaces associated with μ,which,in the case when μ is the d-dimensional Lebesgue measure,also improve the known results.     

Musielak–Orlicz BMO-type Spaces Associated with Generalized Approximations to the Identity

Let X be a space of homogenous type and ψ: X × [0,∞) → [0,∞) be a growth function such that ψ(·,t) is a Muckenhoupt weight uniformly in t and ψ(x,·) an Orlicz function of uniformly upper type 1 and lower type p ∈(0,1].In this article,the authors introduce a new Musielak–Orlicz BMO-type space BMOψA(X) associated with the generalized approximation to the identity,give out its basic properties and establish its two equivalent characterizations,respectively,in terms of the spaces BMOψA,max(X) and BMOψA(X).Moreover,two variants of the John–Nirenberg inequality on BMOψA(X) are obtained.As an application,the authors further prove that the space BMOψΔ1/2(Rn),associated with the Poisson semigroup of the Laplace operator Δ on Rn,coincides with the space BMOψ(Rn) introduced by Ky.     

ENDPOINT ESTIMATES FOR THE COMMUTATOR OF PSEUDO-DIFFERENTIAL OPERATORS

It is well known that the commutator Tb of the Calder′on-Zygmund singular integral operator is bounded on Lp(Rn) for 1 p +∞if and only if b∈BMO [1]. On the other hand, the commutator Tb is bounded from H1(Rn) into L1(Rn) only if the function b is a constant [2]. In this article, we will discuss the boundedness of commutator of certain pseudo-differential operators on Hardy spaces H1. Let Tσbe the operators that its symbol is S01,δwith 0≤δ 1, if b∈LMO∞, then, the commutator [b, Tσ] is bounded from H1(Rn) into L1(Rn) and from L∞(Rn) into BMO(Rn); If [b, Tσ] is bounded from H1(Rn) into L1(Rn) or L∞(Rn) into BMO(Rn), then, b∈LMO_(loc).     

Minimal Hypersurfaces in Hyperbolic Spaces

In this paper, we reprove a theorem of M. Anderson [Invent. Math., 69 （1982）, pp. 477-494] which established the existence of a minimal hypersurface in the hyperbolic space with prescribed asymptotic boundary with non-negative mean curvature in the non-parametric case. We use the mean curvature flow method.     

APPROXIMATION BY WALSH-KACZMARZ-FEJ ′ER MEANS ON THE HARDY SPACE

The main aim of this paper is to find necessary and sufficient conditions for the convergence of Walsh-Kaczmarz-Fej′er means in the terms of the modulus of continuity on the Hardy spaces Hp, when 0〈p≤1/2.     

A Weak Convergence Theorem for A Finite Family of Asymptotically Nonexpansive Mappings

The purpose of this paper is to prove a new weak convergence theorem for a finite family of asymptotically nonexpansive mappings in uniformly convex Banach space.     

COMMON FIXED POINT OF GENERALIZED WEAKLY CONTRACTIVE MAPS IN PARTIAL METRIC SPACES

In this paper, using the context of complete partial metric spaces, some common fixed point results of maps that satisfy the generalized(φ, ψ)-weak contractive conditions are obtained. Our results generalize, extend, unify, enrich and complement many existing results in the literature. Example are given showing the validaty of our results.     

ON SPECTRAL PROPERTIES OF A NEW OPERATOR OVER SEQUENCE SPACES c AND c0

In this work, we classify and calculate spectra such as point spectrum, continuous spectrum and residual spectrum over sequences spaces ?∞, c and c0 according to a new matrix operator W which is obtained by matrix product.     

ASYMPTOTIC DECAY TOWARD RAREFACTION WAVE FOR A HYPERBOLIC-ELLIPTIC COUPLED SYSTEM ON HALF SPACE

We consider the asymptotic behavior of solutions to a model of hyperbolicelliptic coupled system on the half-line R＋ = （0, ∞）,with the Dirichlet boundary condition u（0, t） = 0. S. Kawashima and Y. Tanaka [Kyushu J. Math., 58（2004）, 211-250] have shown that the solution to the corresponding Cauchy problem behaviors like rarefaction waves and obtained its convergence rate when u_ u＋. Our main concern in this paper is the boundary effect. In the case of null-Dirichlet boundary condition on u, asymptotic behavior of the solution （u, q） is proved to be rarefaction wave as t tends to infinity. Its convergence rate is also obtained by the standard L2-energy method and Ll-estimate. It decays much lower than that of the corresponding Cauchy problem.     

Characterizations of Sobolev spaces in Euclidean spaces and Heisenberg groups

Recently, many new features of Sobolev spaces W k,p ？RN ？ were studied in [4-6, 32]. This paper is devoted to giving a brief review of some known characterizations of Sobolev spaces in Euclidean spaces and describing our recent study of new characterizations of Sobolev spaces on both Heisenberg groups and Euclidean spaces obtained in [12] and [13] and outlining their proofs. Our results extend those characterizations of first order Sobolev spaces in [32] to the Heisenberg group setting. Moreover, our theorems also provide diff erent characterizations for the second order Sobolev spaces in Euclidean spaces from those in [4, 5].     

HYPERCYCLIC OPERATORS ON QUASI-MAZUR SPACES

Modifying the method of Ansari,we give some criteria for hypercyclicity of quasi-Mazur spaces.They can be applied to judging hypercyclicity of non-complete and non-metrizable locally convex spaces.For some special locally convex spaces,for example,Ko¨the(LF)-sequence spaces and countable inductive limits of quasi-Mazur spaces,we investigate their hypercyclicity.As we see,bounded biorthogonal systems play an important role in the construction of Ansari.Moreover,we obtain characteristic conditions respectively for locally convex spaces having bounded sequences with dense linear spans and for locally convex spaces having bounded absorbing sets,which are useful in judging the existence of bounded biorthogonal systems.     

Some Fixed Point Results on a Class of Contractive Mappings in Cone Metric Spaces

In this paper, we consider a notion of contractive mappings with certain conditions in cone metric spaces and obtain some results of fixed points by using some necessary conditions. The results directly improve and generalize some fixed point results in metric soaces and some previous results in cone metric spaces.     

BOUNDEDNESS OF FRACTIONAL MAXIMAL OPERATOR AND THEIR HIGHER ORDER COMMUTATORS IN GENERALIZED MORREY SPACES ON CARNOT GROUPS

In the article we consider the fractional maximal operator Mα, 0≤α相似文献   

VARIOUS NOTIONS OF ORTHOGONALITY IN NORMED SPACES

In this paper, we present various notions and aspects of orthogonality in normed spaces. Characterizations and generalizations of orthogonality are also consid-ered. Results on orthogonality of the ran...     

BIFURCATION ANALYSIS IN A GENERALIZED FRICTION MODEL WITH TIME-DELAYED FEEDBACK

In this paper, we consider a generalized model of the two friction models, both of which have two different types of control forces with time-delayed feedback proposed by Ashesh Sara et al. By taking the time delay as the bifurcation parameter, we discuss the local stability of the Hopf bifurcations. Under some condition, the generalized model harbors a phenomenon that the equilibrium may undergo finite switches from stability to instability to stability and finally become unstable. By applying the method introduced by Faria and Magalhaes, we compute the normal form on the center manifold to determine the direction and stability of the Hopf bifurcations. Numerical simulations are carried out and more than one periodic solutions may exist according to the bifurcation diagram given by BIFTOOL. Finally a brief conclusion is presented.     

ATOMIC DECOMPOSITION OF μ-BERGMAN SPACE IN C~n

Let μ be a normal function on [0, 1). The atomic decomposition of the μ-Bergman space in the unit ball B is given for all p 0.     

Commutators of parabolic singular integrals on the generalized Morrey spaces

Let[b,T]be the commutator of parabolic singular integral T.In this paper,the authors prove that the boundedness of[b,T]on the generalized Morrey spaces implies b∈BM O(Rn,ρ).The results in this paper improve and extend the Komori and Mizuhara’s results.     

The Completeness of Cone Metric Spaces

Some topological properties of cone metric spaces are discussed and proved that every cone metric space （X, d） is complete if and only if every family of closed subsets of X which has the finite intersection property and which for every c ε E, 0 〈〈 c contains a set of diameter less that c has non-empty intersection.     

COMPOSITION OPERATORS BETWEEN BLOCH TYPE SPACES IN THE UNIT BALL

In this paper, we obtain some new necessary and suffcient conditions for the boundedness and compactness of composition operators Cφ between Bloch type spaces in the unit ball Bn.