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1.
令ω∈A_1,0αmn和0β1满足条件α+βmn.又设1p_1,…,pm∞使得1/q=1/p-(α+β)/n0并且1/p=1/p_1+…+1/p_m.这时我们有b∈Lip_β(ω)×…×Lip_β(ω)当且仅当由多线性分数次算子I_α与函数向量b生成的线性交换子[Σb,I_α]是从L~(p_1)(ω)×…×L~(p_m)(ω)到L~q(ω~((1-(1-α/n)q))有界的.  相似文献   

2.
一、β_t((?)~n)为{θ(s)|0≤s≤t}所生成的β((?)~n)的子σ-代数,为所有h_t(x,θ):R~ ×R~n×(?)~m→R~d(?)R~r的映射,并且满足 (1)它是β(R~ )×β(R~n)×β((?)~m)|β(R~d(?)R~r)可测的; (2)固定每个t,它是β(R~n)×β((?)~m)|β(R~d(?)R~r)可测的。 这里R~d(?)R~r是全体d×r矩阵,并且赋予它d·r维欧式空间的距离。 C~r(R~n)为R~n上具有r阶连续导数的函数的全体,C_0~r(R~n)为其中具有紧支集的函  相似文献   

3.
一、引言考虑多重线性回归模型Y=Xβ ε,(1)其中,Y=(y_1,…y_n_)′为 n×p 观察矩阵,X=(x_1,…,x_n)′为 n×(k 1)列满秩设计矩阵,β=(β_0,β_1,…β_k)′为(k 1)×p 未知参数矩阵,ε=(ε_1,…ε_n)′为 n×p 随机误差矩阵,ε_1…,ε_n 相互独立.  相似文献   

4.
对0<β_1<β_2≤1,本文得到l~(β_1)的β_2-共轭锥的次表示定理(l~(β_1))_(β_2)~*■m~+×m~+,证明l~(β_1)不是局部β_2-凸空间.  相似文献   

5.
FRACTIONAL INTEGRATION ASSOCIATED TO HIGHER ORDER ELLIPTIC OPERATORS   总被引:1,自引:0,他引:1  
§1. IntroductionLet L be a homogeneous elliptic operator on L2(Rn) of order 2m in divergence formL = (?1)m|α|=|β|=m?α(aα,β?β), (1.1)where we assume aα,β ∈ L∞(Rn;C) for all α,β. The operator L is associated to the followingform Q(f,g) de?ned o  相似文献   

6.
本文主要考虑如下非线性薛定谔方程组的柯西问题:{-iu1t=△u1-μ|u1 |p1u1--α |u1 | q1-2 |u2 |q2u1,(x,t)∈RN×(0,T),-iu2t=△u2-ν |u2 |p2u2-β|u1|q1|u2 | q2-2u2, (x,t)∈RN×(0,T),u1 (x,0)=φ(x),u2(x,0)=φ2(x), x∈RN,其中μ,ν,α,β>0,q1+q2=p3+2,且α/q1=β/q2=b.本文主要研究一些渐近性质,并分别在Sobolev空间、Σ空间及L2(RN)中建立散射理论,这里三={u∈H1(RN),|x|u∈L2 (RN)}.  相似文献   

7.
In this article, we focus on the left translation actions on noncommutative compact connected Lie groups with topological dimension 3 or 4, consisting of SU(2), U(2), SO(3), SO(3)×S~1 and Spin~C(3). We define the rotation vectors(numbers) of the left actions induced by the elements in the maximal tori of these groups, and utilize rotation vectors(numbers) to give the topologically conjugate classification of the left actions. Algebraic conjugacy and smooth conjugacy are also considered. As a by-product, we show that for any homeomorphism f : L(p,-1) × S~1→ L(p,-1) × S~1, the induced isomorphism(π?f?i)_* maps each element in the fundamental group of L(p,-1) to itself or its inverse, where i : L(p,-1) → L(p,-1) × S~1 is the natural inclusion and π : L(p,-1) × S~1→ L(p,-1) is the projection.  相似文献   

8.
In this paper, we introduce Property ∏σ of operator algebras and prove that nest subalgebras and the finite-width CSL subalgebras of arbitrary von Neumann algebras have Property ∏σ.Finally, we show that the tensor product formula alg ML1-(×)algNL2 = algM-(×)N(L1 (×) L2) holds for any two finite-width CSLs L1 and L2 in arbitrary von Neumann algebras M and N, respectively.  相似文献   

9.
子空间的交的基与维数的一种确定方法   总被引:1,自引:0,他引:1  
设V是数域F上n维线性空间,V_1与V_2是它的两个子空间,且 V_1=L(α_1,α_2,…,α_r) V_2=L(β_1,β_2,…,β_s) 于是 V_1 V_2=L(α_1,…,α_r,β_1,…,β_s)故α_1,α_2,…,α_r,β_1,β_2,…,β_s的一个极大线性无关组就是子空间V_1 V_2的一个基,而且 dim(V_1 V_2)=秩(α_1,…,α_r,β_1,…,β_s) 这些都是容易确定的。可以利用矩阵的初等变换方法求得。在一般的高等代数或线性代数的  相似文献   

10.
This note addresses monotonic growths and logarithmic convexities of the weighted((1-t2)αdt2,-∞α∞,0t1)integral means Aα,β(f,)and Lα,β(f,)of the mixed area(πr2)-βA(f,r)and the mixed length(2πr)-βL(f,r)(0≤β≤1 and0r1)of f(rD)and f(rD)under a holomorphic map f from the unit disk D into the finite complex plane C.  相似文献   

11.
Let S∈Rn×n be a symmetric and nontrival involution matrix. We say that A∈E R n×n is a symmetric reflexive matrix if AT = A and SAS = A. Let S R r n×n(S)={A|A= AT,A = SAS, A∈Rn×n}. This paper discusses the following two problems. The first one is as follows. Given Z∈Rn×m (m < n),∧= diag(λ1,...,λm)∈Rm×m, andα,β∈R withα<β. Find a subset (?)(Z,∧,α,β) of SRrn×n(S) such that AZ = Z∧holds for any A∈(?)(Z,∧,α,β) and the remaining eigenvaluesλm 1 ,...,λn of A are located in the interval [α,β], Moreover, for a given B∈Rn×n, the second problem is to find AB∈(?)(Z,∧,α,β) such that where ||.|| is the Frobenius norm. Using the properties of symmetric reflexive matrices, the two problems are essentially decomposed into the same kind of subproblems for two real symmetric matrices with smaller dimensions, and then the expressions of the general solution for the two problems are derived.  相似文献   

12.
本文处理带非线性边界条件 u n=uα, v n=vβ ,(x ,t) ∈ Ω× (0 ,T)的抛物方程组ut =vpΔu ,vt=uqΔv ,(x ,t) ∈Ω× (0 ,T) ,其中Ω RN 为一个有界区域 ,p ,q>0和α ,β≥ 0为常数 .研究了上述问题正解的整体存在性和爆破 ,建立了整体存在和爆破的新标准 .证明了当max{p+β,q+α}≤ 1时正解 (u ,v)整体存在 ,当min{p+β ,q+α}>1且max{α ,β}<1时正解 (u ,v)在有限时刻爆破  相似文献   

13.
In this paper, we introduce Property ∏σ of operator algebras and prove that nest subalgebras and the finite-width CSL subalgebras of arbitrary von Neumann algebras have Property ∏σ.Finally, we show that the tensor product formula alg ML1-(×)algNL2 = algM-(×)N(L1 (×) L2) holds for any two finite-width CSLs L1 and L2 in arbitrary von Neumann algebras M and N, respectively.  相似文献   

14.
Boundedness of Marcinkiewicz integrals and their commutators in H1(Rn×Rm)   总被引:1,自引:0,他引:1  
The authors establish the boundedness of Marcinkiewicz integrals from the Hardy space H1(Rn × Rm) to the Lebesgue space L1(Rn × Rm) and their commutators with Lipschitz functions from the Hardy space H1(Rn × Rm) to the Lebesgue space Lq(Rn × Rm) for some q>1.  相似文献   

15.
建立了一个关于轴对称不可压Navier-Stokes系统的正则性准则.证明了如果局部的轴对称光滑解u满足‖ωr‖Lα1((0,T);Lβ1)+‖ωθ/r‖Lα2((0,T);Lβ2)<∞,其中2/α1+3/β1≤1+3/β1,2/α2+3/β2≤2和β1≥3, β2>3/2,那么此强解将保持光滑性直至时刻T.  相似文献   

16.
Let W(Γ)be a class of not-finitely graded Lie algebras related to gener-alized Virasoro algebras with basis{Lα,i,C | α ∈ Γ,i ∈ Z+},which satisfies relations[Lα,i,Lβ,j]=(β-α)Lα+β,i+j+(j-i)Lα+β,i+j+1+δα+β,0δi+j,0α3-α/12C and[C,Lα,i]=0.In this paper,W(Γ)-modules of the intermediate series satisfying some conditions are con-structed and classified.We also obtain modules of the intermediate series over the related Lie superalgebra.  相似文献   

17.
This paper proves that for Ω∈L(log+L)2(Sn-1×Sm-1), ∫Sn-1 Ω(x′,y′)dσ(x′)=0(y′∈Sm-1),∫Sm-1  Ω(x′,y′)dσ(y′)=0(x′∈Sn-1), the singular integral operator T with kernel K(u,v)=Ω(u′,v′)|u|-n|v|-m is bounded on Lp(Rn×Rm) for 1相似文献   

18.
设H是一实Hillber空间,K是H之一非空间凸子集,设{Ti}Ni=1是N个Lipschitz伪压缩映象使得F=∩Ni=1F(Ti)≠0,其中F(Ti)={x∈K:Tix=x}并且{αn}n∞=1,{βn}∞n=1[0,1]是满足如下条件的实序列(i)∑∞n=1(1-αn)2= ∞;(ii)limn→∞(1-αn)=0;(iii)∑∞n=1(1-βn)< ∞;(iv)(1-αn)L2<1,n1;(v)αn(1-βn)2 αn[βn L(1-βn)]2<1,其中L1是{Ti}iN=1的公共Lipschitz常数,对于x0∈K,设{xn}n∞=1是由下列定义的复合隐格式迭代xn=αnxn-1 (1-αn)Tnyn,yn=βnxn (1-βn)Tnxn,其中Tn=TnmodN,则(i)limn→∞‖xn-p‖存在,对于所有的p∈F;(ii)limn→∞d(xn,f)存在,其中d(xn,F)=infp∈F‖xn-p‖;(iii)liminfn→∞‖xn-Tnxn‖=0.本文的结果推广并且改进H-K.Xu和R.G.Ori在2001年的结果和Osilike在2004年的结果,并且在这篇文章中,主要的证明方法也不同与H-K.Xu和Osilike的方法.  相似文献   

19.
给出并证明格矩阵半群的Euler-Fermat公式:A(n-1)2 1 = A(n-1)2 1 [n], A ∈ Mn(L)其中L是任意的分配格,Mn(L)是L上所有n阶矩阵构成的半群.这是布尔矩阵半群的Euler-Fermat公式的一种推广.  相似文献   

20.
获得如下四阶奇异边值问题{u^(4)(t)-λh(t)f(t,u(t))=0,t∈(0,1),u(0)=u(1)=0,αu^·(0)-βu^·(0)=γu^·(1)+δu^·(1)=0,正解的存在性定理,其中α,β,γ,δ≥0,α+β>0,δ+γ>0,ρ=αγ+γβ+δα>0,参数λ>0,h(t)∈C(0,1)and f∈((0,1)×(0,+∞))文中主要应用全连续算子的逼近技巧和延拓定理以及不动点指数理论.  相似文献   

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