MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

ON COMPACT COMPOSITION OPERATORS ON A CLASS OF HOLOMORPHIC FUNCTION SPACES OVER THE UNIT BALL IN C^n

In this paper, a general function space X（B n ） over the unit ball in C n with norm · X（Bn） is introduced. It contains all Hardy space, Bergman space, Besov space etc. The author gives a formulation of a compact composition operator on X（B n ）, related to works of [8] and [10].

CHAINS OF FUNCTION SPACES OVER EUCLIDIAN SPACES AND LOCAL FIELDS

The Lipschitz class Lip(K, α) on a local field K is defined in [10], and an equivalent relationship between the Ho¨lder type space Cα(K)[9] and Lip(K,α) is given. In this note, we give a 'chain of function spaces' over Euclidian space by defining higher order continuous modulus in R, and point out that there is no need of higher order continuous modulus for describing the chain of function spaces over local fields.

ON THE SELECTION OF SHAPE FUNCTION SPACES OF TRIANGULAR PLATE ELEMENTS

Using the method of undetermined coefficients, we construct a set of shape function spaces of nine-node triangular plate elements converging for any meshes, which generalize Spect's element and Veubeke's element.

Coefficient Multipliers on Some Analytic Function Spaces

In this paper, we give some new results of the coefficient multiplier of some analytic function spaces, characterize the coefficient multiplier spaces (Hα, p Hβ q) and (Ap,α), Aq,β) with 0 < p ≤ 1, p ≤ q ≤∞, 0 ≤α < β < ∞ and show (Hα∞, Hβ∞) = Hβ-α1 with 0 < α < β < ∞.

GLOBAL WELL-POSEDNESSOF A PRANDTL MODEL FROM MHD IN GEVREY FUNCTION SPACES

We consider a Prandtl model derived from MHD in the Prandtl-Hartmann regime that has a damping term due to the effect of the Hartmann boundary layer.A global-in-time well-posedness is obtained in the Gevrey function space with the optimal index 2.The proof is based on a cancellation mechanism through some auxiliary functions from the study of the Prandtl equation and an observation about the structure of the loss of one order tangential derivatives through twice operations of the Prandtl operator.

Regularity of Continuous Linear Operators on Banach Function Spaces

In this paper we present some characterizations of Banach function spaces on which every continuous linear operator is regular.

ON VECTOR-VALUED FUNCTION SPACES WITH HELLY'S PROPERTY

If a vector valued function space with a Hausdorff locally convex topology has a property such that every closed strongly bounded subset is compact, then we name this property Helly's property. In this paper, we show a class of vector valued function spaces with Helly's property and consider convergence of vector measures and best approximations in function spaces in this class.

MULTIPLIERS ON WEIGHTED FUNCTION SPACES OVER LOCALLY COMPACT VILENKIN GROUPS

In this note, we consider the multipliers on weighted function spaces over totally disconnected locally compact abelian groups (Vilenkin groups). Firstly we show an (H1 ,L ) multiplier result. We also give an (Hap ,Hap) multiplier result under a similiar condition of Lu Yang type. In section 2, we obtain a result about the boundedness of multipliers on weighted Besov spaces.

Simulation of γ spectrum-shifting based on the parameter adjustment of Gaussian function space

Based on the statistical characteristics of energy spectrum and the features of spectrum-shifting in spectrometry,the parameter adjustment method of Gaussian function space was applied in the simulation of spectrum-shifting.The transient characteristics of energy spectrum were described by the Gaussian function space,and then the Gaussian function space was transferred by parameter adjustment method.Furthermore,the spectrum-shifting in measurement of energy spectrum was simulated.The applied example shows that the parameters can be adjusted flexibly by this method to meet the various requirements in simulation of energy spectrum-shifting.This method was one parameterized simulation method with good performance for the practical application.

MULTIPLICATION OPERATORS ON INVARIANT SUBSPACES OF FUNCTION SPACES

Let Mφ be the operator of multiplication by φ on a Hilbert space of functions analytic on the open unit disk. For an invariant subspace F for the multiplication operator Mz, we derive some spectral properties of the multiplication operator Mφ ： F→F. We characterize norm, spectrum, essential norm and essential spectrum of such operators when F has the codimension n property with n∈{1,2,...,＋∞}.

On AP-property of Function Spaces

In this paper, it is discussed the AP-property of function spaces. We prove that for any compact network α for a space X which is closed under finite unions, (1) if C α (X) is an AP-space and X is paracompact, then X is a Hurewicz space; (2) if C α (X) is an AP-space which has countable tightness, then C α (X) is discretely generated.

Heredity of Lower Separation Axioms on Function Spaces

The set of continuous functions from topological space Y to topological space Z endowed with a topology forms the function space. For A subset of Y, the set of continuous functions from the space A to the space Z forms the underlying function space with an induced topology. The function space has properties of topological space dependent on the properties of the space Z, such as the T0, T1, T2 and T3 separation axioms. In this paper, we show that the underlying function space inherits the T0, T1, T2 and T3 separation axioms from the function space, and that these separation axioms are hereditary on function spaces.

Function spaces of Besov-type and Triebel-Lizorkin-type——a survey

This article is devoted to presenting a recapitulative introduction for the theory of Besov-type and Triebel-Lizorkin-type spaces developed in recent years.

Representation theorems of the dual of Lebesgue-Bochner function spaces

By representing random conjugate spaces a general representation theorem on classical duals is proved. For application, we unify and improve many known important representation theorems of the dual of Lebesgue-Bochner function spaces.

Weak Hardy-type spaces associated with ball quasi-Banach function spaces I:Decompositions with applications to boundedness of Calderón-Zygmund operators

Let X be a ball quasi-Banach function space on R^(n).In this article,we introduce the weak Hardytype space WH_(X)(R^(n)),associated with X,via the radial maximal function.Assuming that the powered HardyLittlewood maximal operator satisfies some Fefferman-Stein vector-valued maximal inequality on X as well as it is bounded on both the weak ball quasi-Banach function space WX and the associated space,we then establish several real-variable characterizations of WH_(X)(R^(n)),respectively,in terms of various maximal functions,atoms and molecules.As an application,we obtain the boundedness of Calderón-Zygmund operators from the Hardy space H_(X)(R^(n))to WH_(X)(Rn),which includes the critical case.All these results are of wide applications.Particularly,when X:=M^(q)_(p)(R^(n))(the Morrey space),X:=L^(p)(R^(n))(the mixed-norm Lebesgue space)and X:=(EΦq)t(Rn)(the Orlicz-slice space),which are all ball quasi-Banach function spaces rather than quasiBanach function spaces,all these results are even new.Due to the generality,more applications of these results are predictable.

Intrinsic square function characterizations of Hardy spaces associated with ball quasi-Banach function spaces

Let X be a ball quasi-Banach function space satisfying some mild additional assumptions and H x(R n)the associated Hardy-type space.In this article,we first establish the finite atomic characterization of H x(R n).As an application,we prove that the dual space of H x(Rn)is the Campanato space associated with X.For any given a∈(0,1]and s∈Z+,using the atomic and the Littlewood—Paley function characterizations of H x(Rn),we also establish its 5-order intrinsic square function characterizations,respectively,in terms of the intrinsic Lusin-area function S a,s,the intrinsic g-function g a,s,and the intrinsic g*λ-function g*λ,a,s,whereλcoincides with the best known range.

Bessel (Riesz) Potentials on Banach Function Spaces and Their Applications I Theory

In this paper, we shall introduce the concept of the Bessel （Riesz） potential Kothe function spaces Xs （s） and give some dual estimates for a class of operators determined by a semi-group in the spaces Lq （-T, T; Xs） （Lq（-T, T; s ））. Moreover, some time-space LP-LP estimates for the semi-group exp(it（-△）m/2) and the operator A:=∫0t exp(i（t-τ）（-△）m/2). dτ in the Lebesgue-Besov spaces Lq(-T, T; p,2S) are given. On the basis of these results, in a subsequent paper we shall present some further applications to a class of nonlinear wave equations.

The Dichotomy Between Traces on d-sets Г in R^n and the Density of D(R^n\Г) in Function Spaces

A space Apq^s （R^n） with A ： B or A = F and s ∈R, 0 〈 p, q 〈 ∞ either has a trace in Lp（Г）, where Г is a compact d-set in R^n with 0 〈 d 〈 n, or D（R^n／Г） is dense in it. Related dichotomy numbers are introduced and calculated.

Hardy Spaces Associated with Ball Quasi-Banach Function Spaces on Spaces of Homogeneous Type:Littlewood–Paley Characterizations with Applications to Boundedness of Calderón–Zygmund Operators

Let(X,ρ,μ)be a space of homogeneous type in the sense of Coifman and Weiss,and Y(X)a ball quasi-Banach function space on X,which supports both a Fefferman–Stein vector-valued maximal inequality and the boundedness of the powered Hardy–Littlewood maximal operator on its associate space.The authors first introduce the Hardy space H_(Y)(X)associated with Y(X),via the Lusin-area function,and then establish its various equivalent characterizations,respectively,in terms of atoms,molecules,and Littlewood–Paley g-functions and g_(λ)^(*)-functions.As an application,the authors obtain the boundedness of Calderón–Zygmund operators from H_(Y)(X)to Y(X),or to H_(Y)(X)via first establishing a boundedness criterion of linear operators on H_(Y)(X).All these results have a wide range of generality and,particularly,even when they are applied to variable Hardy spaces,the obtained results are also new.The major novelties of this article exist in that,to escape the reverse doubling condition ofμand the triangle inequality ofρ,the authors subtly use the wavelet reproducing formula,originally establish an admissible molecular characterization of H_(Y)(X),and fully apply the geometrical properties of X expressed by dyadic reference points or dyadic cubes.