(p,q)-John椭球

本文主要研究(p,q)-John椭球.经典的John椭球和L_p John椭球均是(p,q)-John椭球的特殊情形.首先讨论(p,q)-John椭球的充分必要条件和连续性.得到了关于(p,q)-John椭球的不等式和包含关系,所得到的不等式和包含关系分别类似于Ball体积比不等式和John包含关系.     

(U(p, q), U(p − 1, q)) is a generalized Gelfand pair

Denote by G = U(p, q) the orthogonal group of the sesqui-linear quadratic form on and let H ₁ = U(p − 1, q) be the stabilizer of the first unit vector e ₁. Let H ₀ = U(1) and set H = H ₀ × H ₁. Define the character χ _l of H by where . Define the anti-involution σ on G by . In this note we show that any distribution T on G satisfying T(h ₁ gh ₂) = χ _l (h ₁ h ₂) T(g) (g ∈ G; h ₁, h ₂ ∈ H) is invariant under the anti-involution σ. This result implies that (G,  H ₁) is a generalized Gelfand pair.      

从β0到E(p,q)和E0(p,q)空间的复合算子

设ψ是单位园盘D到自身的解析映射,X是D上解析函数的Banach空间,对f∈X,定义复合算子Cψ:Cψ(f)=foψ.我们利用从β0到E(p,q)和E0(p,q)空间的复合算子研究了空间E(p,q)和E0(p,q),给出了-个新的特征.     

ELEMENTARY ASPECTS OF B_(p,q)~S(K_n) AND F_(p,q)~S(K_n) SPACFS

In the first part of this paper,we discuss some properties of S~Ω(K_n),L_p~Ω(K_n) andL_p~Ω(K~n;l_a) spaces,give the Plancherel-Polya-Nikol'skij type inequalities and some multipli-er theorems.In the second part of this paper,using the results of Part I we prove some prelimi-nary results for the spaces B_(p,q)~s(K_n) and F_(p,q)~s(K_n).     

关于wF(p,r,q)算子类

作为wA(p,r)算子类的一个推广,该文介绍了一类更广泛的算子类即 wF(p,r,q)算子类,它包含A(p,r)类而含于F(p,r,q)类之中, 进而考虑了该类算子的特征, 包含关系, 正规性和幂性质等等.     

The Central Limit Theorem on SO0(p, q)/SO(p)×SO(q)

We obtain a central limit theorem for the space SO ₀(p, q)/SO(p)×SO(q). To achieve this, we derive a Taylor expansion of the spherical function on the group SO ₀(p, q).     

不等式a~(p q) b~(p q)≥a~pb~q a~qb~p的应用

不等式ａｐ＋ｑ＋ｂｐ＋ｑ≥ａｐｂｑ＋ａｑｂｐ的应用钟成圣（安徽省合肥市中国科大附中２３００２６）定理若ａ，ｂ，ｐ，ｑ∈Ｒ＋，则ａｐ＋ｑ＋ｂｐ＋ｑ≥ａｐｂｑ＋ａｑｂｐ①当且仅当ａ＝ｂ时等号成立．证∵ｐ，ｑ∈Ｒ＋，∴幂函数ｙ＝ｘｐ和ｙ＝ｘｑ在（０，＋∞）...     

ON GENERALIZED COMPLETE(p,q)-ELLIPTIC INTEGRALS

In this paper,we study the generalized complete(p,q)-elliptic integrals of the first and second kind as an application of generalized trigonometric functions with two parameters,and establish the monotonicity,generalized convexity and concavity of these functions.In particular,some Turán type inequalities are given.Finally,we also show some new series representations of these functions by applying Alzer and Richard's methods.     

映入E(q,p)的复合算子

§ 1 .　Introduction　　LetD ={z:｜z｜ <1}betheunitdiskofcomplexplane,H(D)bethespaceofallana lysticfunctionsonD ,denoteLebesguemeasureonDbydm ,normalizedsothatm(D) =1.Fora ∈D ,σa(z) =a-z1- az istheMobiustransformationofDtoitselfandg(z,a) =log｜1- aza-z｜istheGreenfunctionofDwithsingularityata.Everyanalyticself mapφ :D →DoftheunitdiskinducesthroughcompositionalinearcompositionoperatorCφfromH(D)toitself.Itisawell knownconsequenceofLittlewood’ssubordinationprinciple( [1],[2 ])that…     

F(p,q,s)空间的嵌入关系

为得到一类广泛的解析函数空间F(p,q,s)之间的嵌入关系,将每个空间F(p,q,s)对应为三维空间R(F)中一点(p,q,s),从而将空间之间的嵌入关系转化为三维空间中直线的单调性进行了研究,完善了已有的结果.     

GABOR ANALYSIS OF THE SPACES M(p,q,w)(R~d) AND S(p,q,r,w,ω)(R~d)

Let g be a non-zero rapidly decreasing function and w be a weight function. In this article in analog to modulation space, we define the space M(p, q, w)(Rd) to be the subspace of tempered distributions f ∈ S′(Rd) such that the Gabor transform Vg(f) of f is in the weighted Lorentz space L(p, q, wdμ) (R2d). We endow this space with a suitable norm and show that it becomes a Banach space and invariant under time frequence shifts for 1 ≤ p, q ≤ ∞. We also investigate the embeddings between these spaces and the...     

空间B_(p,q)~■与差分法

在[1]中我们引进了 L_p(φ),F_p(φ)空间,在本文中我们把Бесов空间B中的 L_p 范数换为 L_p(φ)范数所得空间记之为 B(φ).我们将把许多 B的结果,拓广到 B(φ)上,主要获得了 B(x)的一个迹定理和差分法在 L_p(φ)中的误差估计.     

WAVELETS AND BESOV SPACES B_(p,q)~s

In this paper we give a new characterization of Besov SpacesB_(q,p)~s,with r-regular (r>0) multiscale analysis.     

Stein流形上(p,q)型Koppelman-Leray-Norguet公式

设M是复n维Stein流形;并设开集D??M具有逐块C¹边界.本文利用陈度量和陈联络,把Stein流形上(0,q)形式的Koppelman-Leray-Norguet公式推广到(p,q)形式,并得到D上?-方程的解.最后,还给出了Stein流形上实非退化强拟凸多面体的Koppelman-Leray-Norguet公式及其?-方程的解.     

空间B_(p,q)~(■)与差分法

在[1]中我们引进了L_p(φ),F_p(φ)空间,在本文中我们把空间B中的L_p范数换为L_p(φ)范数所得空间记之为B(φ)。我们将把许多B的结果,拓广到B(φ)上,主要获得了B(χ)的一个迹     

COMPOSITION OPERATORS FROM B~a TO F(p,q,s)

Necessary and sufficient conditions are given for a composition operator Cof = f o o to be bounded and compact from Ba to F(p, q, s).     

Decomposition Numbers and Cartan Invariants of S p(4,q), q = 2 n,for p = 2*

Let G be the 4-dimensional sympletic group on a finite field of q elements, q a power of 2. We find all the decomposition numbers of G in characteristic 2, corresponding to the unipotent characters of G. We also find some of the Cartan invariants of G for p = 2.     

Cn中空间F(p,q,s)到βq+n+1/p的复合算子

对一切P＞0,s≥0和q＞q＞max{-n-1,-s-1},给出了单位球上一般函数空间F(p,q,s)到Bloch型空间βq+n+1/p之复合算子Cψ有界和紧的充要条件,并给出了几个推论.     

C_(p,q)~(s+α)-forms Solution of _b-equ ation and Its L_(p,q)~s Estimates

§ 1.　Introduction　　TheinhomogeneoustangentialCauchy Riemannoperators,or b complex ,onthebound aryofadomainDinCn(n ≥ 2 ) ,hasplayedanimportantroleinthestudyofboundaryvaluesofholomorphicfunctionsandholomorphicextensioninCn(examplesseeKOHNandROSSI[3] ,AndrettiandHILL [4] ) .In 1 977,HENKIN [1 ]wasfirstlyobservedthat,if b equa tions bu =fon Dissolvable ,the (p ,1 ) form ,f ,0≤ p≤ 2 ,mustsatisfythecompatibilitycondition∫ Df∧Ψ =0forall b closed (2 p ,0 ) formsΨonDinwhich…     

Compact Ceshro Operators from Spaces H（p,q,u） to H（p, q, v）

Abstract Let μ and ν be normal functions and let T _g be the extended Cesàso operator in terms of the symbol g. In this paper, we will characterize those g so that T _g is bounded (or compact) from mixed norm spaces H(p, q, μ) to H(p, q, ν) in the unit ball of C ⁿ . Furthermore, as applications, some analogous results are also given on weighted Bergman spaces and Dirichlet type spaces. Supported by the National Natural Science Foundation of China (No.10571049, 10471039), the Natural Science Foundation of Zhejiang Province (No. M103085).