从人力车看近代上海城市公共交通的演变

18 74年人力车传入上海后 ,一度实现了对轿子等旧式交通工具的超越 ,推动了城市公共交通的发展。虽然人力车的种种优势使其在机械化公共交通工具被引入之后仍然在上海的公共交通中扮演重要角色 ,但是 ,作为一种依靠人力拉动的交通工具 ,人力车的废除又是历史的必然。然而 ,在近代上海独特的社会背景之下 。

Loewner Chains Associated with the Generalized Roper-Suffridge Extension Operator on the Unit Ball in Hilbert Spaces

In this paper, we prove that the generalized Roper-Suffridge extension operator can be embeded in Loewner chains on the unit ball in Hibert spaces, and obtain the fact that the operator keeps the properties of almost spirallike mapping of typeβ and order α, almost starlikeness of order α, spirallikeness of type ofβ and starlikeness.

On Maximal, Discrete, and Area Operators

In this paper, we study the boundednesses of maximal operator g., the discrete operator gd, and the area operator A on Bergman spaces.

Finite Operators

Let H be a separable infinite dimensional complex Hilbert space, and L（H） the algebra of all bounded linear operators on 3-t＇. The class of finite operators is the class of operators for which the distance of the identity operator I and the derivation range is maximal; where the derivation range of the operator A is defined by δA;δA ： L（H） -L（H） X- AX - XA. In this paper we present some properties of finite operators and give some classes of operators which are in the class of finite operators, and find for witch condition A ~ W is a finite operator in L（2-H H）, and gave a g6neralisation of Stampflli theorem.

Loewner Chains Associated with the Generalized Roper-Suffridge Extension Operator

In this paper, we prove that the generalized Roper-Suffridge extension operator can be embedded in Loewner chains on the unit ball in Hibert spaces, and obtain the fact that the operator keeps the properties of almost spirallike mapping of type β and other α, almost staxlikeness of order α, spirallikeness of type β and starlikeness.

Approximation Properties For Modified Kantorovich-Type Operators

We introduce a modification of Kantorovich-type operators in polynomial weighted spaces of functions. Then we study some approximation properties of these operators. We give some inequalities for these operators by means of the weighted modulus continuity and also obtain a Voronovskaya-type theorem. Furthermore, in our paper show that the operators give better degree of approximation of functions belonging to weighted spaces than classical Szaisz- Kantorovich operators.

Endpoint estimates for n-dimensional Hardy operators and their commutators

In this paper,the sharp bound for the weak-type(1,1) inequality for the n-dimensional Hardy operator is obtained.Moreover,the precise norms of generalized Hardy operators on the type of Campanato spaces are worked out.As applications,the corresponding norms of the Riemann-Liouville integral operator and the n-dimensional Hardy operator are deduced.It is also proved that the n-dimensional Hardy operator maps from the Hardy space into the Lebesgue space.The endpoint estimate for the commutator generated by the Hardy operator and the(central) BMO function is also discussed.

Applications of Orlicz-Hardy spaces associated with operators satisfying Poisson estimates

Let L be a linear operator in L^2（R^n） and generate an analytic semigroup {e^-tL}t≥0 with kernel satisfying an upper bound estimate of Poisson type, whose decay is measured by θ（L） ∈ （0, ∞）. Let 4） be a positive, continuous and strictly increasing function on （0, ∞）, which is of strictly critical lower type pФ （n/（n ＋ θ（L））, 1]. Denote by HФ, L（R^n） the Orlicz-Hardy space introduced in Jiang, Yang and Zhou＇s paper in 2009. If Ф is additionally of upper type 1 and subadditive, the authors then show that the Littlewood-Paley g-function gL maps HФ, L（R^n） continuously into LФ（R^n） and, moreover, the authors characterize HФ, L（R^n） in terms of the Littlewood-Paley gλ^＊-function with λ ∈ （n（2/pФ ＋ 1）, ∞）. If Ф is further slightly strengthened to be concave, the authors show that a generalized Riesz transform associated with L is bounded from HФ, L（R^n） to the Orlicz space L^Ф（R^n） or the Orlicz-Hardy space HФ （R^n）; moreover, the authors establish a new subtle molecular characterization of HФ, L （R^n） associated with L and, as applications, the authors then show that the corresponding fractional integral L^-γ for certain γ∈ E （0,∞） maps HФ, L（R^n） continuously into HФ, L（R^n）, where Ф satisfies the same properties as Ф and is determined by Ф and λ and also that L has a bounded holomorphic functional calculus in HФ, L（R^n）. All these results are new even when Ф（t） = t^p for all t ∈ （0, ∞） and p ∈ （n/（n ＋ θ（L））, 1].

Hardy spaces H_L^p(R^n) associated with operators satisfying k-Davies-Gaffney estimates

Let L be a one-to-one operator of type w having a bounded H∞ functional calculus and satisfying the k-Davies-Gaffney estimates with k C N. In this paper, the authors introduce the Hardy space HPL（Rn） with p ∈（0, 1] associated with L in terms of square functions defined via {e-t2kL}t〉O and establish their molecular and generalized square function characterizations. Typical examples of such operators include the 2k-order divergence form homogeneous elliptic operator L1 with complex bounded measurable coefficients and the 2k-order Schr6dinger type operator L2 ：= （-△）k ＋ Vk, where A is the Laplacian and 0≤V C Llkoc（Rn）. Moreover, as an application, for i E {1, 2}, the authors prove that the associated Riesz transform Vk（Li-1/2） p n HP（Rn） for @ （n/（n ＋ k）, 1] and establish the Riesz transform characterizations is bounded from HLI（IR ） to p of HPL1（]Rn） for p C （rn/（n ＋ kr）, 1] if {e-tL1 }t〉o satisfies the Lr - L2 k-off-diagonal estimates with r C （1, 2]. These results when k ：= I and L ：= L1 are known.

Volterra operator, area integral and Carleson measures

We characterize the boundedness of Volterra operators from Bergman spaces to Hardy spaces. Area integral operators and Carleson measures are heavily involved.

Weighted integral inequalities in Orlicz martingale classes

Under appropriate conditions on Young's functions Φ1 and Φ2,we give necessary and sufficient conditions in order that weighted integral inequalities hold for Doob's maximal operator M on martingale Orlicz setting.When Φ1 = tp and Φ2 = tq,the inequalities revert to the ones of strong or weak(p,q)-type on martingale space.

A new approach to the time evolution of characteristic function of the density operator obtained by virtue of thermal entangled state representation

Like the progress made by Dirac that wave function ψ(x) was reformed as x |ψ,where x| is the coordinate representation,we endow the characteristic function χλ = Tr(e λa-λaρ) of density operator ρ with the meaning of wave function of |ρ in the thermal entangled state η| representation in the doubled Fock space,χλ = η = λ|ρ,where |ρ = ρ|η = 0.We find the time evolution of χλ can then be directly and neatly obtained via this approach.The way of deriving the density operator from η = λ | ρ is also presented.

Hausdorff Operators on Function Spaces

The authors mainly study the Hausdorff operators on Euclidean space Rn. They establish boundedness of the Hausdorff operators in various function spaces, such as Lebesgue spaces, Hardy spaces, local Hardy spaces and Herz type spaces. The results reveal that the Hausdorff operators have better performance on the Herz type Hardy spaces HKP（Rn） than their performance on the Hardy spaces Hv（Rn） when 0 〈 p 〈 1. Also, the authors obtain some new results and reprove or generalize some known results for the high dimensional Hardy operator and adjoint Hardy operator.

A local version of Hardy spaces associated with operators on metric spaces

Let （X, d, μ） be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ. Let L be a second order self-adjoint positive operator on L^2（X）. Assume that the semigroup e-^tL generated by -L satisfies the Gaussian upper bounds on L2（X）. In this article we study a local version of Hardy space hi （X） associated with L in terms of the area function characterization, and prove their atomic characters. Furthermore, we introduce a Moser type local boundedness condition for L, and then we apply this condition to show that the space hzL（X） can be characterized in terms of the Littlewood-Paley function. Finally, a broad class of applications of these results is described.

On Radon-Penrose transformation and k-Cauchy-Fueter operator

It is known that there is a 1-1 correspondence between the first cohomology of the sheaf O(-k-2) over the projective space and the solutions to the k-Cauchy-Fueter equations on the quaternionic space Hn.We find an explicit Radon-Penrose type integral formula to realize this correspondence:given a -closed(0,1)form f with coefficients in the(-k-2)th power of the hyperplane section bundle H-k-2,there is an integral representation Pf such that ι*(Pf) is a solution to the k-Cauchy-Fueter equations,where ι is an embedding of the quaternionic space Hn into C4n.

Additional symmetries of constrained CKP and BKP hierarchies

The additional symmetries of the constrained CKP (cCKP) and BKP (cBKP) hierarchies are given by their actions on the Lax operators, and their actions on the eigenfunction and adjoint eigenfunction {Φ i , Ψ i } are presented explicitly. Furthermore, we show that acting on the space of the wave operator, *k forms new centerless W cC 1+∞ and W cB 1+∞ -subalgebra of centerless W 1+∞ respectively. In order to define above symmetry flows *k of the cCKP and cBKP hierarchies, two vital operators Y k are introduced to revise the additional symmetry flows of the CKP and BKP hierarchies.

Similarity invariants of operators on a class of Gowers-Maurey spaces

This paper studies the similarity invariants of operators on a class of Gowers-Maurey spaces, ∑dc spaces, where an infinite dimensional Banach space X is called a ∑dc space if for every bounded linear operator on X the spectrum is disconnected unless it is a singleton. It shows that two strongly irreducible operators T1 and T2 on a ∑dc space are similar if and only if theK0-group of the commutant algebra of the direct sum T1 GT2 is isomorphic to the group of integers Z. On a ∑dc space X, it uses the semigroups of the commutant algebras of operators to give a condition that an operator is similar to some operator in （∑SI）（X）, it further gives a necessary and sufficient condition that two operators in （∑SI）（X） are similar by using the ordered K0-groups. It also proves that every operator in （∑SI）（X） has a unique （SI） decomposition up to similarity on a ∑dc space X, where （∑SI）（X） denotes the class of operators which can be written as a direct sum of finitely many strongly irreducible operators.

Modulation space estimates for the fractional integral operators

We obtain the boundedness for the fractional integral operators from the modulation Hardy space μp,q to the modulation Hardy space μr,q for all 0 < p < ∞. The result is an extension of the known result for the case 1 < p < ∞ and it contains a larger range of r than those in the classical result of the Lp → Lr boundedness in the Lebesgue spaces. We also obtain some estimates on the modulation spaces for the bilinear fractional operators.

Commutators of Calderón-Zygmund operators related to admissible functions on spaces of homogeneous type and applications to Schrdinger operators

Let X be an RD-space. In this paper, the authors establish the boundedness of the commutator Tbf = bTf-T(bf) on Lp , p∈(1,∞), where T is a Calderón-Zygmund operator related to the admissible function ρ and b∈BMOθ(X)BMO(X). Moreover, they prove that Tb is bounded from the Hardy space H1ρ(X) into the weak Lebesgue space L1weak(X). This can be used to deal with the Schrdinger operators and Schrdinger type operators on the Euclidean space Rn and the sub-Laplace Schrdinger operators on the stratified Lie group G.

Totally compatible associative and Lie dialgebras,tridendriform algebras and PostLie algebras

This paper studies the concepts of a totally compatible dialgebra and a totally compatible Lie dialgebra,defined to be a vector space with two binary operations that satisfy individual and mixed associativity conditions and Lie algebra conditions respectively.We show that totally compatible dialgebras are closely related to bimodule algebras and semi-homomorphisms.More significantly,Rota-Baxter operators on totally compatible dialgebras provide a uniform framework to generalize known results that Rota-Baxter related operators give tridendriform algebras.Free totally compatible dialgebras are constructed.We also show that a Rota-Baxter operator on a totally compatible Lie dialgebra gives rise to a PostLie algebra,generalizing the fact that a Rota-Baxter operator on a Lie algebra gives rise to a PostLie algebra.