齐次群上Herz型Hardy空间的分解

本文建立了齐次群上Herz型Hardy空间的原子和分子分解特征．作为其应用,研究了中心δ-Calderon-Zygmund算子在这些Hardy空间上的有界性．     

Classical Fourier Analysis over Homogeneous Spaces of Compact Groups

This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G andμ be the normalized G-invariant measure on G/ H associated to the Weil's formula.Then, we present a generalized abstract framework of Fourier analysis for the Hilbert function space L~2(G/H,μ).     

两点齐性的Finsler流形

该文证明任何一个两点齐性的Finsler流形一定是黎曼流形．证明过程中作者将泛函分析中经典的Mazur定理推广到不一定是绝对齐次的Minkowski空间上．     

Quantum Cohomology of Minuscule Homogeneous Spaces

We study the quantum cohomology of (co)minuscule homogeneous varieties under a unified perspective. We show that three points Gromov–Witten invariants can always be interpreted as classical intersection numbers on auxiliary varieties. Our main combinatorial tools are certain quivers, in terms of which we obtain a quantum Chevalley formula and a higher quantum Poincaré duality. In particular, we compute the quantum cohomology of the two exceptional minuscule homogeneous varieties. DOI: .     

齐型空间上的Herz空间及其应用

定义了一类齐型空间上的Herz空间及弱Herz空间,研究了定义在这些空间中的一类次线性算子的性质．     

Discrete Approximation of Spaces of Homogeneous Type

In this note we combine the dyadic families introduced by M. Christ in (Colloq. Math. 60/61(2):601–628, 1990) and the discrete partitions introduced by J.M. Wu in (Proc. Am. Math. Soc. 126(5):1453–1459, 1998) to get approximation of a compact space of homogeneous type by a uniform sequence of finite spaces of homogeneous type. The convergence holds in the sense of a metric built on the Hausdorff distance between compact sets and on the Kantorovich-Rubinshtein metric between measures. The authors were supported by CONICET, CAI+D (UNL) and ANPCyT.     

On the Commutativity of Weakly Commutative Riemannian Homogeneous Spaces

A Riemannian homogeneous space X=G/H is said to be commutative if the algebra of G-invariant differential operators on X is commutative and weakly commutative if the associated Poisson algebra is commutative. Clearly, the commutativity of X implies its weak commutativity. The converse implication is proved in this paper.     

齐型空间上L1与 BMO的内插空间

本文讨论齐型空间上L~1与BMO的内插空间,得到下列结果:对于0<θ<1,1≤q≤∞,有(L~1,BMO)_(θ,q)=L_(pq),其中θ=1-1/p.     

Riesz Potentials in Besov and Triebel–Lizorkin Spaces over Spaces of Homogeneous Type

By using the discrete Calderón reproducing formulae, the author first establishes the boundedness of the Riesz-potential-type operator in homogeneous Besov and Triebel–Lizorkin spaces over spaces of homogeneous type. Then, by use of the T1 theorems for these spaces, the author proves that this operator of Riesz potential type can be used as the lifting operator of these spaces.     

Some of Commutators on Spaces of Homogeneous Type

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｌｅｔａｂｅａｍｅａｓｕｒａｂｌｅｆｕｎｃｔｉｏｎ ,ｂｅａ φ∈Ｓ(Ｒ)ｎｏｎｎｅｇａｔｉｖｅｆｕｎｃｔｉｏｎ ,ａｎｄ 0 <ｒ <∞ .Ｄｅｆｉｎｅｃｏｍｍｕｔａｔｏｒｓａｓｆｏｌｌｏｗｓ :Ｃｒａ( ｆ) (ｘ) =ｓｕｐｘ∈Ｑ1｜Ｑ｜∫Ｑ｜ａ(ｘ) -ａ( ｙ) ｜ｒ｜ｆ( ｙ) ｜ｄｙ ,( 1 .1 )ａｎｄΦｒａ( ｆ) (ｘ) =ｓｕｐε>0∫Ｒｎ｜ａ(ｘ) -ａ( ｙ) ｜ｒφε( ｜ｘ- ｙ｜)｜ｆ( ｙ) ｜ｄｙ ,( 1 .2 )ｗｈｅｒｅＱｄｅｎｏｔｅｓａｃｕｂｅａｎｄφε(ｔ) =1εｎφ ｔε .Ｔｈｅｓｅｔｗｏｏｐｅｒａｔ…     

分数次积分算子的交换子在齐型空间上的弱型估计

本文研究分数次积分交换子,其中Kα(x,y)=d(x,y)α-1,m∈N且b(x)∈BMO(X,μ),证明了Iα,bm是从Orlicz空间L(log L)m(X)到弱Lq(X)空间的映照．同时还证明了分数次极大算子交换子Mα,bm也有类似性质．     

A Structure Theorem for Homogeneous Spaces

A partial generalization of Sophus Lie’s triangular form for solvable Lie algebras is presented. As application one is led to an iterated fibration for arbitrary homogeneous spaces. In the case of compact homogeneous spaces, one concludes easily that the Euler number is ≥0.     

Integration of Geodesic Flows on Homogeneous Spaces: The Case of a Wild Lie Group

We obtain necessary and sufficient conditions for the integrability in quadratures of geodesic flows on homogeneous spaces M with invariant and central metrics. The proposed integration algorithm consists in using a special canonical transformation in the space T ^* M based on constructing the canonical coordinates on the orbits of the coadjoint representation and on the simplectic sheets of the Poisson algebra of invariant functions. This algorithm is applicable to integrating geodesic flows on homogeneous spaces of a wild Lie group.     

Embeddings of Spherical Homogeneous Spaces

We review in these notes the theory of equivariant embeddings of spherical homogeneous spaces. Given a spherical homogeneous space G/H, the normal equivariant embeddings of G/H are classified by combinatorial objects called colored fans, which generalize the fans appearing in the classification of toric varieties and which encode several geometric properties of the corresponding variety.     

Nonlinear Bound States on Weakly Homogeneous Spaces

We prove the existence of ground state solutions for a class of nonlinear elliptic equations, arising in the production of standing wave solutions to an associated family of nonlinear Schrödinger equations. We examine two constrained minimization problems, which give rise to such solutions. One yields what we call F _λ-minimizers, the other energy minimizers. We produce such ground state solutions on a class of Riemannian manifolds called weakly homogeneous spaces, and establish smoothness, positivity, and decay properties. We also identify classes of Riemannian manifolds with no such minimizers, and classes for which essential uniqueness of positive solutions to the associated elliptic PDE fails.     

齐型空间上$L^1$ 与{\rm BMO}的内插空间

本文讨论齐型空间上$L^1$ 与{\rm BMO}的内插空间, 得到下列结果:对于本文讨论齐型空间上$L^1$ 与{\rm BMO}的内插空间, 得到下列结果:对于本文讨论齐型空间上$L^1$ 与{\rm BMO}的内插空间, 得到下列结果:对于摘要：本文讨论齐型空间上L^1与BMO的内插空间，得到下列结果：对于0〈θ〈1，1≤q≤∞，有（L^1，BMO）θ，q=Lpq，其中θ=1-1/p。     

Minimal Homogeneous Submanifolds in Euclidean Spaces

We prove that minimal (extrinsically) homogeneous submanifolds of the Euclidean space are totally geodesic. As an application, we obtain that a complex homogeneous submanifold of C ^N must be totally geodesic.     

Affine Versions of Singer's Theorem on Locally Homogeneous Spaces

A theorem of Singer says that an infinitesimaly homogeneous Riemannian manifold is locally homogeneous. We propose two result on affine connections similar to the theorem of Singer. As an application we prove a theorem giving a sufficient condition for local homogeneity in case of affine connections on 2-dimensional manifolds.     

齐型空间上的Lipschitz函数空间

给出了齐型空间上Lipschitz函数空间的两个新的等价范数，证明了Lipschitz函数满足与BMO函数类似的Joho-Nirenberg型不等式．