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.     

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).     

ELLIPTIC GRADIENT ESTIMATES FOR DIFFUSION OPERATORS ON COMPLETE RIEMANNIAN MANIFOLDS

In this note,we obtain the elliptic estimate for diffusion operator L=△+φ on complete,noncompact Riemannian manifolds,under the curvature condition C D(K,m),which generalizes B.L.Kotschwar's work [5].As an application,we get estimate on the heat kernel.The Bernstein-type gradient estimate for Schro¨dinger-type gradient is also derived.     

NEW SPECTRAL CHARACTERIZATIONS OF EXTREMAL HYPERSURFACES

Let M be a closed extremal hypersurface in Sn+1 with the same mean curva-ture of the Willmore torus Wm,n?m. We proved that if Specp(M)=Specp(Wm,n?m) for p=0, 1, 2, then M is Wm,m.     

Maximum Principle for Nonlinear Cooperative Elliptic Systems on R^N

We investigate in this work necessary and sufficient conditions for having a Maximum Principle for a cooperative elliptic system on the whole R^N. Moreover, we prove the existence of solutions by an approximation method for the considered system.     

AREA INTEGRAL FUNCTIONS AND H∞ FUNCTIONAL CALCULUS FOR SECTORIAL OPERATORS ON HILBERT SPACES

Area integral functions are introduced for sectorial operators on Hilbert spaces. We establish the equivalence relationship between the square and area integral functions. This immediately extends McIntosh/Yagi＇s results on H∞ functional calculus of sectorial operators on Hilbert spaces to the case when the square functions are replaced by the area integral functions.     

Fuzzy Rough Ring and Its Properties

This paper is devoted to the theories of fuzzy rough ring and its properties. The fuzzy approximation space generated by fuzzy ideals and the fuzzy rough approximation operators were proposed in the frame of fuzzy rough set model. The basic properties of fuzzy rough approximation operators were analyzed and the consistency between approximation operators and the binarv operation of ring was discussed.     

FINITE ELEMENT APPROXIMATION OF AN INTEGRO-DIFFERENTIAL OPERATOR

This paper deals with the finite element approximation of an integro-differential equation related with Riemann zeta-function.     

UNIQUENESS, ERGODICITY AND UNIDIMENSIONALITY OF INVARIANT MEASURES UNDER A MARKOV OPERATOR

Let X be a compact metric space and C（X） be the space of all continuous functions on X. In this article, the authors consider the Markov operator T ： C（X）N C（X）N defined by
for any f = （f1,f2,… ,fN）, where （pij） is a N x N transition probability matrix and {wij } is an family of continuous transformations on X. The authors study the uniqueness, ergodicity and unidimensionality of T＊-invariant measures where T＊ is the adjoint operator of T.     

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...     

BOUNDEDNESS FROM BELOW OF MULTIPLICATION OPERATORS BETWEEN α-BLOCH SPACES ON THE UNIT BALL

In this article,we characterize the boundedness from below of multiplication operators between α-Bloch spaces on the unit ball.     

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   

WEIGHTED COMPOSITION OPERATORS ON WEIGHTED DIRICHLET SPACES

We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.     

AREA INTEGRAL FUNCTIONS FOR SECTORIAL OPERATORS ON L^p SPACES

Area integral functions are introduced for sectorial operators on Lp-spaces. We establish the equivalence between the square and area integral functions for sectorial operators on Lpspaces. This follows that the results of Cowling, Doust, McIntosh, Yagi, and Le Merdy on H∞functional calculus of sectorial operators on Lp-spaces hold true when the square functions are replaced by the area integral functions.     

BOUNDEDNESS OF STEIN＇S SQUARE FUNCTIONS ASSOCIATED TO OPERATORS ON HARDY SPACES

Let(X, d, μ) be a metric measure space endowed with a metric d and a nonnegative Borel doubling measure μ. Let L be a second order non-negative self-adjoint operator on L2(X). Assume that the semigroup e-tLgenerated by L satisfies the Davies-Gaffney estimates. Also, assume that L satisfies Plancherel type estimate. Under these conditions,we show that Stein's square function Gδ(L) arising from Bochner-Riesz means associated to L is bounded from the Hardy spaces Hp L(X) to Lp(X) for all 0 p ≤ 1.     

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.     

APPROXIMATING SOLUTION OF 0∈ T（x） FOR AN H-MONOTONE OPERATOR IN HILBERT SPACES

The purpose of this paper is to study the solution of 0 ∈ T (x) for an H-monotone operator introduced in [Fang and Huang, Appl. Math. Comput. 145(2003)795-803] in Hilbert spaces, which is the first pro...     

THE NAVIER-STOKES EQUATIONS WITH THE KINEMATIC AND VORTICITY BOUNDARY CONDITIONS ON NON-FLAT BOUNDARIES

We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition （without the incompressibility condition）, which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in R^n（n ≥ 3） with nonhomogeneous vorticity boundary condition converge in L^2 to the corresponding Euler equations satisfying the kinematic condition.     

EXISTENCE OF ENTROPY SOLUTIONS TO TWO-DIMENSIONAL STEADY EXOTHERMICALLY REACTING EULER EQUATIONS

We are concerned with the global existence of entropy solutions of the twodimensional steady Euler equations for an ideal gas, which undergoes a one-step exothermic chemical reaction under the Arrhenius-type kinetics. The reaction rate function φ(T) is assumed to have a positive lower bound. We first consider the Cauchy problem(the initial value problem), that is, seek a supersonic downstream reacting flow when the incoming flow is supersonic, and establish the global existence of entropy solutions when the total variation of the initial data is suffciently small. Then we analyze the problem of steady supersonic, exothermically reacting Euler flow past a Lipschitz wedge, generating an additional detonation wave attached to the wedge vertex, which can be then formulated as an initial-boundary value problem. We establish the global existence of entropy solutions containing the additional detonation wave(weak or strong, determined by the wedge angle at the wedge vertex) when the total variation of both the slope of the wedge boundary and the incoming flow is suitably small. The downstream asymptotic behavior of the global solutions is also obtained.     

WELL-POSEDNESS OF A COMPRESSIBLE GAS-LIQUID MODEL FOR DEEPWATER OIL WELL OPERATIONS

The main purpose of this paper is two-fold:(i) to generalize an existence result for a compressible gas-liquid model with a friction term recently published by Friis and Evje [SIAM J. Appl. Math., 71(2011), pp. 2014–2047];(ii) to derive a uniqueness result for the same model. A main ingredient in the existence part is the observation that we can consider weaker assumptions on the initial liquid and gas mass, and still obtain an existence result. Compared to the above mentioned work, we rely on a more refined application of the estimates provided by the basic energy estimate. Concerning the uniqueness result, we borrow ideas from Fang and Zhang [Nonlinear Anal. TMA, 58(2004), pp. 719–731] and derive a stability result under appropriate constraints on parameters that determine rate of decay toward zero at the boundary for gas and liquid masses, and growth rate of masses associated with the friction term and viscous coefficient.