Dm型正交代数的极大幂零子代数上保零李括积的映射

令F表示任意域,l_(2m)(F)表示F上D_m型正交李代数的极大幂零子代数.本文的目的是当m≥5时,刻画l_(2m)(F)上的每一个双向保零李括积的映射.利用文献[7]的主要结果和矩阵计算技巧,本文证明了l_(2m)(F)上的一个线性映射φ是双向保零李括积的当且仅当φ能够写成内自同构,图自同构,广义的对角自同构,中心映射,次中心自同构,极端映射和标量乘法的乘积.这推广了文献[7]的主要结果.     

Embeddable quantum homogeneous spaces

We discuss various notions generalizing the concept of a homogeneous space to the setting of locally compact quantum groups. On the von Neumann algebra level we recall an interesting duality for such objects studied earlier by M. Izumi, R. Longo, S. Popa for compact Kac algebras and by M. Enock in the general case of locally compact quantum groups. A definition of a quantum homogeneous space is proposed along the lines of the pioneering work of Vaes on induction and imprimitivity for locally compact quantum groups. The concept of an embeddable quantum homogeneous space is selected and discussed in detail as it seems to be the natural candidate for the quantum analog of classical homogeneous spaces. Among various examples we single out the quantum analog of the quotient of the Cartesian product of a quantum group with itself by the diagonal subgroup, analogs of quotients by compact subgroups as well as quantum analogs of trivial principal bundles. The former turns out to be an interesting application of the duality mentioned above.     

Characterizing sequences for precompact group topologies

Motivated from [31], call a precompact group topology τ on an abelian group G ss-precompact (abbreviated from single sequence precompact  ) if there is a sequence u=(_un)$\mathbf{u}=(u_n)$ in G such that τ is the finest precompact group topology on G   making u=(_un)$\mathbf{u}=(u_n)$ converge to zero. It is proved that a metrizable precompact abelian group (G,τ)$(G,\tau )$ is ss-precompact iff it is countable. For every metrizable precompact group topology τ on a countably infinite abelian group G there exists a group topology η such that η is strictly finer than τ   and the groups (G,τ)$(G,\tau )$ and (G,η)$(G,\eta )$ have the same Pontryagin dual groups (in other words, (G,τ)$(G,\tau )$ is not a Mackey group in the class of maximally almost periodic groups).     

Muckenhoupt weights with singularities on closed lower dimensional sets in spaces of homogeneous type

We give sufficient conditions on a real number β and on a closed set F   in a general space of homogeneous type (X,d,μ)$(X,d,\mu )$ in such a way that μ(B(x,d(x,F)))^β$\mu {(B(x,d(x,F)))}^{\beta }$ becomes a Muckenhoupt weight. In order to prove our result, we modify the underlying space so that it becomes 1-Ahlfors regular.     

Lorentz spaces with variable exponents

We introduce Lorentz spaces and with variable exponents. We prove several basic properties of these spaces including embeddings and the identity . We also show that these spaces arise through real interpolation between and . Furthermore, we answer in a negative way the question posed in 12 whether the Marcinkiewicz interpolation theorem holds in the frame of Lebesgue spaces with variable integrability.     

齐次Morrey-Herz空间中高阶交换子的中心BMO估计

建立了具有粗糙核的Hardy—Littlewood极大算子高阶交换子及其相应的分数次极大算子高阶交换子在齐次Morrey-Herz空间上的中心BMO估计,并由此得到了由一类次线性算子所生成的高阶交换子在齐次Morrey—Herz空间上的相应结果.     

Rough singular integrals associated with surfaces of Van der Corput type简

In this paper,the authors establish the Lp-mapping properties for a class of singular integrals along surfaces in Rn of the form {φ(|u|)u : u ∈ Rn} as well as the related maximal operators provided that the function φ satisfies certain oscillatory integral estimates of Van der Corput type,and the integral kernels are given by the radial function h ∈Δγ(R+) for γ 1 and the sphere function Ω∈ Fβ(Sn.1) for some β 0,which is distinct from H1(Sn.1).     

抛物型方程初边值问题解的最大模估计

通过构造合适函数变换的方法,建立n维抛物型方程第二初边值问题古典解的最大模估计,并由此得到该定解问题解的唯一性和稳定性.     

Riemann-Stieltjes积分边值问题正解的存在唯一性

利用解的先验估计和极值原理,研究了一类具有Riemann-Stieltjes积分边值问题正解的存在唯一性．     

Calderón–Zygmund Operators in the Bessel Setting for All Possible Type Indices

We show that many harmonic analysis operators in the Bessel setting,including maximal operators,Littlewood–Paley–Stein type square functions,multipliers of Laplace or Laplace–Stieltjes transform type and Riesz transforms are,or can be viewed as,Calderón–Zygmund operators for all possible values of type parameter λ in this context.This extends results existing in the literature,but being justified only for a restricted range of λ.