Bloch空间上的Cesaro算子是有界的

记B={f:f∈H(D),‖f‖B＜∞}为Bloch空间，其中‖f‖B=sup |x|＜1(1-|z|^2)|f′(z)|,对于f(z)=^∞∑(k-0)akz^k∈B，定义Cesaro算子B为(Bf)(z)=^∞∑(n=0)(1/(n 1) ^n∑(k=0)ak)z^n在这篇文章中，我们将证明如下结果。     

一类高阶线性微分方程解的增长性

本文研究了在Aj(z),aj(j=0,1,…,k-1)满足一些条件下方程f(k)+Ak-1(z)eak-1f(k-1)+…+A0(z)ea0zf=0解的超级和在Aj(z),Pj(j)(j=0,1,…,k-1)满足一些条件下方程f(k)+Ak-1(z)ePk-1(z)f(k-1)+…+Aj(z)eajzf(j)+…+A0(z)eP0(z)f=0解的级。     

Use Cesro Means To Describe Two Classes of Functions

Let H(D)be the collection of functions which are analytic in the unitdisc D.we call B_0={f∈H(D),(?)(1-|z|~2)|f’(z)|=0}litlle Bloch space.Letf∈H(D),0相似文献   

一类高阶整函数系数微分方程解的增长级、下级与超级

该文研究了一类高阶整函数系数微分方程解的增长性,对方程f~(k)+A_(k-1)(z)e~(ak-1z).f~(k-1)+…+A_0(z)e~(a0z)f=0与方程f~(k)+(A_(k-1)(z)e~(ak-1z)+D_(k-1)(z))f~(k-1)+…+(A_0(z)e~(a0z)+D_0(z))f=0中a_j(0≤j≤k-1)幅角主值不全相等的情形,得到了解的增长级、下级与超级的精确估计.     

单位球上不同Bergman空间之间小Hankel算子的本性模

本文利用指标φ的Berezin变换给出了小Hankel算子hφ:Ap(B)→Aq(B)(1 p∞,1q∞,p q)的本性模估计C1lim sup|a|→1-|Vφ(a)|∥hφ∥e,Ap(B)→Aq(B)C2lim sup|a|→1-|Vφ(a)|,∫其中Vφ(a)=∫B{k2(1+1/p-1/q)(w,a)1}/K1+1/p-1/q(a,a)φ(w)dν(w),C1和C2是常数.作为应用,本文给出了此类算子有界当且仅当supa∈B|Vφ(a)|∞,而此类算子是紧的当且仅当lim sup|a|→1-|Vφ(a)|=0.     

多复变数完全拟凸映射的分解定理

设Ω_1C~(n1),Ω_2C~(n2)为凸的Reinhardt域,f(z,w)=(f1(z,w),f2(z,w))'为Ω_1×Ω_2上的正规化全纯映射.本文证明f为Ω_1×Ω_2上的正规化双全纯完全拟凸映射当且仅当 f(z,w)=(Φ_1(z),Φ_2(w))'其中φj:Ωj→C~(nj)是Ωj(j=1,2)上的正规化双全纯完全拟凸映射。     

多复变数完全拟凸映射的分解定理

设Ω1(∪) Cn1,Ω2(∪)Cn2为凸的Reinhardt域,f(z,w)=(f1(z,w),f2(z,w))′为Ω1×Ω2上的正规化全纯映射.本文证明f为Ω1×Ω2上的正规化双全纯完全拟凸映射当且仅当f(z,w)=(Φ1(z),Φ2(W))′,其中ΦjΩj→Cnj是Ωj(j=1,2)上的正规化双全纯完全拟凸映射.     

A NEW ROPER-SUFFRIDGE EXTENSION OPERATOR ON BOUNDED COMPLETE REINHARDT DOMAINS

In this paper, we construct a new Roper-Suffridge extension operator Φr n,β1,,βn(f)(z) = F(z) = ((rf(z1/r)/z1)β1z1,(rf(z1/r)/z1)β2z2,...,(rf(z1/r)/z1)βnzn)',where f is a normalized locally biholomorphic function on the unit disc D, r = sup{|z1| : z =(z1, ···, zn) ∈Ω}, β1∈ [0, 1], 0 ≤βk≤β1, k = 2, ···, n, then we prove it can preserve the property of spirallikeness of type β, almost starlikeness of order α and starlikeness of orderα on bounded complete Reinhardt domain Ω, respectively.     

系数的级相同的高阶微分方程解的增长性

In this paper,we consider the growth of solutions of some homogeneous and nonhomogeneous higher order differential equations.It is proved that under some conditions for entire functions F,A_(ji) and polynomials P_j(z),Q_j(z)(j=0,1,…,k-1;i=1,2)with degree n≥1,the equation f~(k)+(A_(k-1,1)(z)e~(p_(k-1)(z))+A_(k-1,2)(z)e~(Q_(k-1(z)))/~f~(k-1)+…+(A_(0,1)(z)e~(P_o(z))+A_(0,2)(z)e~(Q_0(z)))f=F,where k≥2,satisfies the properties:When F ≡0,all the non-zero solutions are of infinite order;when F=0,there exists at most one exceptional solution fo with finite order,and all other solutions satisfy λ(f)=λ(f)=σ(f)=∞.     

On the Growth of Solutions of a Class of Higher Order Linear Differential Equations

In this paper, we investigate the growth of solutions of the differential equations f(k)+Ak?1(z)f(k?1)+· · ·+A0(z)f =0, where Aj(z)(j=0, · · · , k?1) are entire functions. When there exists some coe?cient As(z)(s ∈ {1, · · · , k?1}) being a nonzero solution of f00+P(z)f =0, where P(z) is a polynomial with degree n(≥1) and A0(z) satisfiesσ(A0)≤1/2 or its Taylor expansion is Fabry gap, we obtain that every nonzero solution of such equations is of infinite order.     

NUMERICAL SOLUTIONS OF DISCONTINUOUS BOUNDARY VALUE PROBLEMS FOR GENERAL ELLIPTIC COMPLEX EQUATIONS OF FIRST ORDER

1Formulati0nofDiscontinuousBoundaryValueProblemsLetDbeanN 1-connectedb0undeddomaininthez=x iy-planeCwiththeboundaryFEC:(0相似文献   

一类高阶线性微分方程解的增长性

本文讨论一类一般的齐次和非齐次高阶线性微分方程解的增长性,证明了当整函数F,A_j,D_j和s≥1次多项式P_j(z)(j=0,1,…,k-1)满足某些条件时,方程(其中k≥2),f~(k) (A_(k-1)(z)e~(P_(k-1)(z)) D_(k-1)(z))f~((k-1)) … (A_0(z)e~(P_0(z)) D_0(z))f=F当F≡0时,所有非零解具无穷级；当F≠0时,至多除去一个有限级解f_0外,其余所有解均满足■(f)=λ(f)=σ(f)=∞且σ_2(f)≤max{s,σ(F)},从而推广了M．Frei,M．Ozawa,G．Gundersen,J．K．Langley,陈宗煊,李纯红等人的结果。     

与Hayman不等式相联系的奇异方向

以下是Hayman 的基本不等式:设f(z)是区域|z|相似文献   

高阶亚纯函数系数微分方程的解及其导数的不动点

研究了高阶线性微分方程f~(k)+A_(k-1)(z)f~(k-1)+…+A_1(z)f′+A_0(z)f=0的非零解f,及其一阶、二阶导数,f~(i)(i=1,2)的不动点性质,这里A_j(z)(j=0,1,…k-1)为亚纯函数,得到了若δ(∞,A_0)>0,且满足max{i(A1),i(A2),…,i(A_(k-1))}相似文献   

Q_p空间中的Jackson定理

在Qp空间上建立了Jackson型不等式,即对任意f(z)=Σ∞(j=0)ajzj∈Qp,0≤p<∞,a>1及k-1∈N,有||f(z)-Γk/Γ(k+a)Σ(k-1)(j=0)Γ(k-j+a)/Γ(k-j)ajzj||Qp≤C(a)ω(1/k,f,Qp),其中ω(1/k,f,Qp)为Qp空间中的连续模,C(a)是仅与参数a有关的正常数。     

ON A PROBLEM IN COMPLEX OSCILLATION THEORY OF PERIODIC HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

In this article, the zeros of solutions of differential equation f(k)(z)+A(z)f(z) = 0, (*) are studied, where k 2, A(z) = B(ez), B(ζ) = g1(1/ζ) + g2(ζ), g1 and g2 being entire functions with g2 transcendental and σ(g2) not equal to a positive integer or infinity. It is shown that any linearly independent solutions f1, f2, . . . , fk of Eq.(*) satisfy λe(f1 . . . fk) ≥σ(g2) under the condition that fj(z) and fj(z+ 2πi) (j = 1, . . . , k) are linearly dependent.     

分担值与正规族

设F是平面区域D上的亚纯函数族,a,b是两个有穷非零复数.如果(A)f∈F,f(z)=a(=)f(k)(z)=a,f(k)(z)=b(=)f(k+1)(z)=b,且f-a的零点重数至少为k(k≥3),那么函数族F在D内正规;当k=2时,在条件a≠4b的情况下,同样有函数族F在D内正规.     

关于高阶线性微分方程解的增长性

在本文中,我们研究了一类高阶齐次线性微分方程f(k) +Ak-1f(k-1)+…+Aof=0,其中Aj(z) (j=0,1,…,k-1)是有限级整函数,且存在As(z)(s∈{0,1,…,k-1))是超越的且σ(As)＜1/2或其泰勒展式为缺项级数.我们给出了方程任一解f(≠)0的增长估计.     

THE VALUE DISTRIBUTION AND UNIQUENESS OF ONE CERTAIN TYPE OF DIFFERENTIAL-DIFFERENCE POLYNOMIALS

In this article, we investigate the distribution of the zeros and uniqueness of differential-difference polynomials G(z) =(fn(fm(z)- 1)dΠj=1f(z + cj)vj)(k)- α(z),H(z) =(fn(f(z)- 1)mdΠj=1f(z + cj)vj)(k)- α(z),where f is transcendental entire function of finite order, cj(j = 1, 2, ···, d), n, m, d, and vj(j = 1, 2, ···, d) are integers, and obtain some theorems, which extended and improved many previous results.     

一类高阶线性微分方程解的增长性

研究一类高阶线性微分方程f(k)+Hk-1f(k-1)+…+H1f'+ H0f=0解的性质,其中Hj=Aj1(z)ePj1(z)+Aj2(z)ePj2(z)(j=0,1,…,k-1),Pjq(q=1,2)是n次复系数多项式,Ajq(z)是级小于n的整函数,当Pjq首项系数的主幅角不全相等时,得到这类方程的超越解有无穷级且超级为n.