A WEIGHTED ESTIMATE OF THE HORMANDER MULTIPLIER ON THE HEISENBERG GROUP

In this article, the authors prove the weighted boundedness of Hormander-type multiplier on the Heisenberg group.     

SL(3,3~n)和SU(3,3~n)的第一Cartan不变量

确定Cartan不变量是代数群与相关的李型有限群的模表示理论中的一个重要方面.作者利用代数群模表示理论中的一系列结果,计算了3~n个元素的有限域上特殊线性群SL(3,3~n)和特殊酉群SU(3,3~n)的第一Cartan不变量,得到如下结论:当G=SL(3,3~n)时,C_(00)~((n))=a~n+b~n+6~n-2·8~n;而当G=SU(3,3~n)时,C_(00)~((n))=a~n+b~n+6~n-2·8~n+2·(1+(-1)~n),其中a,b是多项式x~2-20x+48的两个根.另外,作者也得到了射影不可分解模U_n(0,0)的维数公式:dim U_n(0,0)=(12~n-6~n+∈)·3~(3n),其中,当G=SL(3,3~n)时,∈=1;而当G=SU(3,3~n)时,∈=-1.     

有界对称域上混合范数空间的乘子变换

本文考虑了Ｃ＾ｎ中有界对称域Ω上的混合范数空间Ｈｐ，ｑ，ａ（Ω）它包含许多重要的函数空间，如Ｈａｒｄｙ空间、Ｂｅｒｇｍａｎ空间、缓慢增长的函数空间以及Ｂｐｑ，研究了Ｈｐ，ｑ，ａ（Ω）中函数的现人类 乘子变 得到了Ｈｐ，ｑ，ａ（Ω）中的Ｈａｒｄｙ－Ｌｉｔｔｌｅｗｏｏｄ定理。这些结果均推了以前一系列结论。     

TRANSFERENCE OF MAXIMAL MULTIPLIER OPERATORS ON LOCAL HARDY-LORENTZ SPACES

§1. IntroductionLet Hp(Rn), 0 < p < ∞be the Hardy spaces de?ned by Hp(Rn) = f ∈S (Rn) : sup|?t ? f| < ∞, t>0 Lp(Rn)where ? ∈S(Rn), ? = 1 and ?t(x) =     

区域上Triebel-Lizorkin空间的原子分解与限制定理

本文在区域Ω( Rn,n≥1)上定义了某类在边界上消失的Triebel-Lizorkin空间 ,并给出了它的原子分解定理,对偶定理.同时证明了当区域 时,得到了限制和扩张定理     

THE SPHERICAL FUNCTIONS AND THE CENTRAL LIMIT THEOREM ON SU(2,2)/S(U(2)×U(2))

Let G = SU(2,2), K = S(U(2)×U(2)), and for l∈Z, let {τl}l∈z be a onedimensional K-type and let El be the line bundle over G/K associated to τl. It is shown that the τl-spherical function on G is given by the hypergeometric functions of several variables. By applying this result, a central limit theorem for the space G/K is obtained.     

A WEIGHTED ESTIMATE OF THE HOERMANDER MULTIPLIER ON THE HEISENBERG GROUP

In this article, the anthors prove the weighted boundedness of Hoermander-type multiplier on the Heisenberg group.     

THE REALIZATION OF MULTIPLIER HILBERT BIMODULE ON BIDUAL SPACE AND TIETZE EXTENSION THEOREM

51. Introduction and PreliminaryThe multiplier bimodule of imprimitive bimodule and its application to coaction systemwere introduced in [if, but it is generally not an imprimitive bimodule as noted in [II by anexample. In this paper, the same concept is introduced for Hilbert bimodules which properlycontain imprimitive bimodules (for example, the same example as above), and we obtainthe realization of multiplier bimodule on a quotient of bidual space and Tietze extensiontheorem similar to t…     

Besov 空间上的算子插值定理

本文研究了算子的插值问题.利用Riesz-Thorin定理的证明方法,并运用Daubechies小波得到了Besov空间上的线性算子的插值定理.     

ON THE PRIMARY DECOMPOSITION THEOREM OF MODULAR LIE SUPERALGEBRAS

This gives some identities of associative Lie superalgebras and some properties of modular Lie superalgebras. Furthermore, the primary decomposition theorem of modular Lie superalgebras is shown. It is well known that the primary decomposition theorem of modular Lie algebras has played an important role in the classification of the finite-dimensional simple modular Lie algebras (see [5, 6]). Analogously, the primary decomposition theorem of modular Lie superalgebras may play an important role in the open classification of the finite dimensional simple modular Lie superalgebras.     

小波与函数空间

Triebe利用Littlewood Paley分解将大多数函数空间分类成两类三指标的函数空间：Besov空间和Triebel Lizorkin空间；但Littlewood Paley 分解很难直接分析Sobolev空间L^p的插值空间Lorentz空间，也很难分析Triebel Lizorkin空间F^{α,q}_1的预备对偶空间和对偶空间.运用小波，作者给出这些空间一个统一刻画：Triebel Lizorkin Lorentz 空间，Besov Lorentz空间和F^{α,q}_1的预备对偶空间和对偶空间；另外也研究这些空间的三个性质.     

ON PJATECKII-SAPIRO PRIME NUMBER THEOREM

ＯＮ ＰＪＡＴＥＣＫＩI－SＡＰＩＲＯ ＰＲＩＭＥ ＮＵＭＢＥＲ ＴＨＥＯＲＥＭ ￥ＪＩＡＣＨＡＯＨＵＡＡｂｓｔｒａｃｔ：Ｉｔｉｓｐｒｏｖｅｄｔｈａｔ，ｆｏｒ１＜ｃ＜ｅ，ｔｈｅｒｅａｒｅｉｎｆｉｎｉｔｅｌｙｍａｎｙｐｒｉｍｅｓｏｆｔｈｅｆｏｒｍ［ｎ＇ｌ...     

Deforming abelian SU(2)-representations of knot groups

The aim of this paper is to generalize a theorem of C. D. Frohman and E. P. Klassen ([FK91]) concerning deformations of abelian SU(2)-representations of knot groups into non-abelian representations. The proof of our main theorem makes use of a generalization of a result of X.-S. Lin ([Lin92]) which should be interesting in itself. Received: December 1, 1997     

DISTORTION THEOREM FOR BIHOLOMORPHICMAPPINGS IN TRANSITIVE DOMAINS(IV)

ＤＩＳＴＯＲＴＩＯＮＴＨＥＯＲＥＭＦＯＲＢＩＨＯＬＯＭＯＲＰＨＩＣＭＡＰＰＩＮＧＳＩＮＴＲＡＮＳＩＴＩＶＥＤＯＭＡＩＮＳ（ＩＶ）￥ＺＨＥＮＧＸＵＥＡＮ；ＧＯＮＧＳＨＥＮＧＡｂｓｔｒａｃｔ：Ｔｈｅｄｉｓｔｏｒｔｉｏｎｔｈｅｏｒｅｍｆｏｒｂｉｈｏｌｏｍｏ...     

SU(3)-manifolds of cohomogeneity one

In this article, we classify 7- and 8-dimensional manifolds M admitting an SU(3) action of cohomogeneity one such that (i) M is simply connected and the orbit space M/G is isomorphic to [0, 1], and (ii) \({M/G\cong S^{1}}\) and the principal orbits are simply connected. We discuss applications to the study of the group manifold SU(3) and to 8-dimensional quaternion-Kähler spaces, and links between dimension 7 and 8 given by circle actions.     

Carnot群上一类半线性方程的Liouville型定理

本文研究了Carnot群上一类具有超线性非齐次项的半线性次Laplace方程非负解的存在性问题.结合Birindelli等[4]在Heisenberg群上利用积分不等式研究解的方法和拟齐性分析技巧,给出了此类方程在Carnot群上的一类Liouville型定理.     

局部紧的Vilenkin群上的加权局部Hardy空间

该文给出了Vilenkin群上加权局部Hardy空间的定义,它的原子分解及对偶性质,并且研究了一类卷积算子在其上的有界性．     

ON THE CONDITIONAL VERSION OF KOLMOGOROV'S THREE-SERIES THEOREM

1991MRSubjectClassification60F15,6()G251IntroductionItiswellknownthatKolnlogorov'sthree-seriestheoremplaysasoleroleinprobabilitytheory.NotonlydoesitI)resentsacompleteanswertothequestionofconvergenceforindependentr.v.'s,butalsoyeildssatisfactoryforltlofstronglawoflargenurllbers.Thesllffi(:ielltp;trtofthetlleorenlisalsotrueinthedependellt(:ases.ifwetakethecollditiolitllProbabilities,(:oil'litiollalexpectatiollswithrespecttothepastillsteadoftileI)robabilities,ed)ectzttiollsrespe('tivelyinthet…     

Equivariant Spectral Triples on the Quantum SU(2) Group

We characterize all equivariant odd spectral triples for the quantum SU(2) group acting on its L ₂-space and having a nontrivial Chern character. It is shown that the dimension of an equivariant spectral triple is at least three, and given any element of the K-homology group of SU_q(2), there is an equivariant odd spectral triple of dimension 3 inducing that element. The method employed to get equivariant spectral triples in the quantum case is then used for classical SU(2), and we prove that for p < 4, there does not exist any equivariant spectral triple with nontrivial K-homology class and dimension p acting on the L ₂-space.The first author would like to acknowledge support from the National Board of Higher Mathematics, India.