Uniform Homeomorphisms of Unit Spheres and Property H of Lebesgue–Bochner Function Spaces

Assume that the unit spheres of Banach spaces X and Y are uniformly homeomorphic.Then we prove that all unit spheres of the Lebesgue–Bochner function spaces L_p(μ, X) and L_q(μ, Y)are mutually uniformly homeomorphic where 1 ≤ p, q ∞. As its application, we show that if a Banach space X has Property H introduced by Kasparov and Yu, then the space L_p(μ, X), 1 ≤ p ∞,also has Property H.     

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.     

Variable 2-Microlocal Besov–Triebel–Lizorkin-Type Spaces

This article is devoted to the study of variable 2-microlocal Besov-type and Triebel–Lizorkin-type spaces. These variable function spaces are defined via a Fourier-analytical approach. The authors then characterize these spaces by means of φ-transforms, Peetre maximal functions, smooth atoms, ball means of differences and approximations by analytic functions. As applications, some related Sobolev-type embeddings and trace theorems of these spaces are also established. Moreover, some obtained results, such as characterizations via approximations by analytic functions, are new even for the classical variable Besov and Triebel–Lizorkin spaces.     

Boundedness for Hardy Type Operators on Herz Spaces with Variable Exponents

In this paper, we will prove the boundedness of Hardy type operators Hβ(x) and H*β(x) of variable order β(x) on Herz spaces Kα(·)p(·),q and Kα(·)p(·),q' where α(·) and p(·)are both variable.     

CARLESON MEASURES,RIEMANN-STIELTJES OPERATORS AND MULTIPLIERS ON F(p,q,s)SPACES IN THE UNIT BALL OF C~n

This paper is devoted to characterizing the Riemann-Stieltjes operators and pointwise multipliers on F(p,q,s) spaces in the unit ball of C~n,which contain many classical function spaces,such as the Bloch space,BMOA and Q_s spaces.The boundedness and compactness of these operators on F(p,q,s) spaces are characterized by means of an embedding theorem,i.e.,F(p,q,s) spaces boundedly embedded into the tent-type spaces T_(p,s)~∞(μ).     

Complex Interpolation of Weighted Besov and Lizorkin–Triebel Spaces

We study complex interpolation of weighted Besov and Lizorkin–Triebel spaces.The used weights w0,w1 are local Muckenhoupt weights in the sense of Rychkov.As a first step we calculate the Calder′on products of associated sequence spaces.Finally,as a corollary of these investigations,we obtain results on complex interpolation of radial subspaces of Besov and Lizorkin–Triebel spaces on Rd.     

Fo ck-Sob olev Spaces and Weighted Comp osition Op erators among Them

We characterize the boundedness and compactness of weighted composition operators among some Fock-Sobolev spaces. We also estimate the norm and essential norm of these operators. Furthermore, we discuss the duality spaces of FockSobolev spaces F_s~(p,m) when 0 p ∞.     

与截面相关的Morrey空间与奇异积分

In this paper, we define the Morrey spaces M_F~(p,q) (Rn) and the Campanato spaces E_F~(p,q) (R~n) associated with a family F of sections and a doubling measure μ, where F is closely related to the Monge-Amp`ere equation. Furthermore, we obtain the boundedness of the Hardy-Littlewood maximal function associated to F, Monge-Amp`ere singular integral operators and fractional integrals on M_F~(p,q)(R~n). We also prove that the Morrey spaces M_F~(p,q) (R~n)and the Campanato spaces E_F~(p,q) (R~n) are equivalent with 1 ≤ q ≤ p ∞.     

DOMAIN OF THE DOUBLE SEQUENTIAL BAND MATRIX B（r,s） ON SOME MADDOX＇S SPACES

The domain of generalized difference matrix B(r, s) in the classical spaces l∞,c, and c0 was recently studied by Kirisci and Bassar in [16]. The main goal of this article is to introduce the paranormed sequence spaces l∞( B, p), c( B, p), and c0( B, p), which are more general and comprehensive than the corresponding consequences of the matrix domain of B(r, s), as well as other studies in literature. Besides this, the alpha-, beta-, and gamma-duals of the spaces l∞( B, p), c( B, p), and c0( B, p) are computed and the bases of the spaces c( B, p)and c0( B, p) are constructed. The final section of this article is devoted to the characterization of the classes(λ( B, p) :) and( : λ( B, p)), where λ∈ {c, c0, l∞}and is any given sequence space. Additionally, the characterization of some other classes which are related to the space of almost convergent sequences is obtained by means of a given lemma.     

Commutators of hardy type operators on Herz spaces with variable exponents北大核心CSCD

We mainly prove the boundedness of the commutators of Hardy type operators on Herz spaces Kp(·),qα(·), where α(·) and p(·) are both variable. ©, 2015, Chinese Academy of Sciences. All right reserved.     

Toeplitz Products on Bergman–Sobolev Spaces over the Unit Polydisk

In this paper, we characterize the compactness and Fredholmness of Toeplitz operators and Toeplitz products on Bergman–Sobolev spaces over the unit polydisk. We also calculate the essential norm of finite sums of finite Toeplitz products on these spaces.     

THE BOUNDEDNESS FOR A CLASS OF ROUGH FRACTIONAL INTEGRAL OPERATORS ON VARIABLE EXPONENT LEBESGUE SPACES

In this paper,we will discuss the behavior of a class of rough fractional integral operators on variable exponent Lebesgue spaces,and establish their boundedness from L p 1 (·) (R n) to L p 2 (·) (R n).     

Some specific unboundedness property in smoothness Morrey spaces. The non-existence of growth envelopes in the subcritical case

We study smoothness spaces of Morrey type on Rn and characterise in detail those situations when such spaces of type A_(p,q)~(s,r)(R~n) or A_(u,p,q)~s(R~n) are not embedded into L_(∞)(R~n).We can show that in the so-called sub-critical,proper Morrey case their growth envelope function is always infinite which is a much stronger assertion.The same applies for the Morrey spaces M_(u,p)(R~m) with p u.This is the first result in this direction and essentially contributes to a better understanding of the structure of the above spaces.     

EXTENSION OF ISOMETRIES BETWEEN THE UNIT SPHERES OF COMPLEX lp(Γ)(p > 1) SPACES

In this paper, we study the extension of isometries between the unit spheres of complex Banach spaces lp(Γ) and lp(△)(p 1). We first derive the representation of isometries between the unit spheres of complex Banach spaces lp(Γ) and lp(△). Then we arrive at a conclusion that any surjective isometry between the unit spheres of complex Banach spaces lp(Γ)and lp(△) can be extended to be a linear isometry on the whole space.     

Time-decay Estimates for Keller–Segel System

For the Cauchy problem to Keller–Segel system, we show well-posedness and time-decay estimates in the critical scaling-invariant Besov spaces by using Littlewood–Paley analysis together with the decay estimates of heat kernels.     

On some new paranormed euler sequence spaces and Euler Core

In this paper, the sequence spaces e0^τ（u, p） and ec^τ（u, p） of non-absolute type which are the generalization of the Maddox sequence spaces have been introduced and it is proved that the spaces e0^τ（u,p） and ec^τ（u,p） are linearly isomorphic to spaces co（p） and c（p）, respectively. Furthermore, the α-, β- and γ-duals of the spaces 0^τ（u,p） and ec^τ（u,p） have been computed and their bases have been constructed and some topological properties of these spaces have been investigated. Besides this, the class of matrices （e0^τ）（u, p） ： μ） has been characterized, where μ is one of the sequence spaces l∞, c and co and derives the other characterizations for the special cases of μ. In the last section, Euler Core of a complex-valued sequence has been introduced, and we prove some inclusion theorems related to this new type of core.     

Herz-type Hardy spaces on Vilenkin groups and their applications

Let 1＜q＜∞, 1-1/q≤α＜∞, 0＜p＜∞ and G be a locally compact Vilenkin group.The authors first introduce the general Herz-type Hardy spaces HKα,pq(G) and hKα,pq(G), then present the central atom or the central block and atom decompositions of these spaces. Using this characterization, they discuss some properties of these spaces and investigate the boundedness on the spaces HKα,pq(G) of the fractional integral operators and the boundedness on the spaces hKα,pq(G) of the pseudo-differential operators of order zero.     

Perturbations of Moore–Penrose Metric Generalized Inverses of Linear Operators in Banach Spaces

In this paper,the perturbations of the Moore–Penrose metric generalized inverses of linear operators in Banach spaces are described.The Moore–Penrose metric generalized inverse is homogeneous and nonlinear in general,and the proofs of our results are different from linear generalized inverses.By using the quasi-additivity of Moore–Penrose metric generalized inverse and the theorem of generalized orthogonal decomposition,we show some error estimates of perturbations for the singlevalued Moore–Penrose metric generalized inverses of bounded linear operators.Furthermore,by means of the continuity of the metric projection operator and the quasi-additivity of Moore–Penrose metric generalized inverse,an expression for Moore–Penrose metric generalized inverse is given.     

实值函数与某些覆盖性质

In the paper [properties defined with semi-continuous functions and some related spaces',Houston J.Math.,2015,41(3):1097–1106] properties(U L)~(wl)_m,(U L)~K_m and(U L)_m were defined and it was shown that spaces having these properties coincide with countably paracompact spaces,countably mesocompact spaces and countably metacompact spaces,respectively.In this paper,we continue with the study on the relationship between properties defined with real-valued functions and some covering properties.Some characterizations of countably compact spaces and pseudo-compact spaces in terms of real-valued functions are obtained.     

The Boundedness of Composition Operators on Triebel–Lizorkin and Besov Spaces with Different Homogeneities

In this paper, we introduce new Triebel–Lizorkin and Besov Spaces associated with the different homogeneities of two singular integral operators. We then establish the boundedness of composition of two Calder′on–Zygmund singular integral operators with different homogeneities on these Triebel–Lizorkin and Besov spaces.