共查询到20条相似文献,搜索用时 31 毫秒
1.
对 0<α <∞, Nα 是开单位圆盘 D 上满足 sup z∈ D(1-|z|2)α f# (z)<∞ 的亚纯函数类, 其中 f# (z)=|f'(z)|/(1+|f(z)|2) 是 f 的球面导数. 该文给出了 D 上的 α -正规函数类的一些积分准则, 并用 Bergman-Carleson 测度的形式予以表示. 相似文献
2.
A. Yu. Solynin 《Journal of Mathematical Sciences》1996,79(5):1341-1358
We consider the class S1(τ), 0<τ<1, of functions f(z)=rz+a2z2+... that are regular and univalent in the unit disk U and have |f(z)|<1. We obtain sharp estimates for the 1-measure of the
sets {θ: |f(eiθ)|=1}. As a corollary, for the familiar class S we find Kolmogorov-type estimates for the sets {θ: |f(eiθ)|>M}, M>1, and prove inequalities for the harmonic measure, which are similar to those by Carleman-Milloux and Baernstein.
We also consider problems on distortion of fixed systems of boundary arcs in the classes of functions that are regular (or
meromorphic) and univalent in the disk or circular annulus. Bibliography: 23 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 204, 1993, pp. 115–142.
Translated by A. Yu. solynin. 相似文献
3.
面积平均p叶函数的最小模估计及其应用 总被引:1,自引:1,他引:0
假设,在单位圆盘△={z:|z|<1}内是面积平均p叶函数.关于|f'/f|2的平均增长,Hayman和Duren等对其进行了详细的研究.注意到,这种增长涉及到f(z)的最小模m(r)=min|z|=r|f(z)|.本文首先估计m(r),然后给出一些相关的应用,其中包括|f'/f|2的平均增长估计,|f(eiθ)|-λ的可积性以及一个新的Bazilevic定理,这个新的定理涉及到f的最大增长方向和最小增长方向.我们得到的某些结果是不可改进的. 相似文献
4.
The role that a prescribed holomorphic Hopf (Quadratic) differential A(z) dz dz plays in the construction of a negatively
curved immersed simply connected complete surface ∑0
of prescribed constant mean curvature c ∈ (−1, 1)in the hyperbolic 3-Space
H
3
is investigated in this work. When a holomorphic function A(z), which is the coefficient function of the Hopf differential,
is prescribed on a unit disk |z| < 1,it is shown that the unit disk |z| < 1can be immersed in the hyperbolic 3-Space
H
3
as a negatively curved complete surface of constant mean curvature c ∈ (−1, 1),provided that |A(z)| satisfies a certain growth condition. Moreover, it is shown that the unit disk |z| < 1can be uniquely embedded in
H
3
when the holomorphic function A(z) has a certain admissible structure. 相似文献
5.
K. -J. Wirths 《Constructive Approximation》1999,15(3):427-440
In this paper we construct Bloch functions F for which the set {z | e sup
|ζ| < 1
|F'(ζ)| ( 1 - |ζ|
2
) = |F'(z)| ( 1 - |z|
2
)} is an analytic Jordan curve tangential to the unit disk in some points. It is proved that, using such functions, we can
derive analogs to the Taylor expansion for Bloch functions in cases where the Taylor expansion does not converge.
October 15, 1997. Date revised: March 12, 1998. Date accepted: June 18, 1998. 相似文献
6.
L. V. Kovalev 《Journal of Mathematical Sciences》2002,110(6):3111-3120
A simple proof of the recent result by E. G. Emel'yanov concerning the maximum of the conformal radius r(D,1) for a family of simply connected domains with a fixed value r(D,0) is given. A similar problem is solved for a family of convex domains. Exact estimates for functionals of the form
are obtained for families of functions inverse to elements of the classes S and Sm, where S={f:f is regular and univalent in the disk {z:|z| < 1} and f(0)=f'(0)-1=0} and SM=
for
. Bibliography: 7 titles. 相似文献
7.
YangChangsen 《高校应用数学学报(英文版)》2001,16(3):285-289
Abstract. Suppose H is a complex Hilbert space, AH (△) denotes the set of all analytic operator functions on 相似文献
8.
《复变函数与椭圆型方程》2012,57(7):553-563
Let D denote the open unit disk and $ f:D \to \bar {{\bf C}}$ be meromorphic and injective in D . Especially, we consider such f which have an expansion $$ f(z) = z + \sum \limits_{n=2}^{\infty }a_n(\;f\,)z^n $$ in a neighbourhood of the origin and map D onto a domain whose complement with respect to $\bar {{\bf C}}$ is convex. Let the set of these functions be denoted by Co . We fix | f m 1 ( X )| for f ] Co and determine the inner and outer radius of the ring domain which is the domain of variability of a 2 ( f ) for such f . Further, it is shown that f ] Co implies that $$ \phi (z) = z+2 {f'(z) \over f''(z)}$$ is holomorphic in D and maps D into itself. This implication in turn implies the inequalities | a n ( f )| S 1 for f ] Co and n = 2,3,4. In addition, we show that | a n ( f )| S 1/2 for f ] Co and all n S 2 . 相似文献
9.
Let U(λ, μ) denote the class of all normalized analytic functions f in the unit disk |z| < 1 satisfying the condition
$
\frac{{f(z)}}
{z} \ne 0and\left| {f'(z)\left( {\frac{z}
{{f(z)}}} \right)^{\mu + 1} - 1} \right| < \lambda ,\left| z \right| < 1.
$
\frac{{f(z)}}
{z} \ne 0and\left| {f'(z)\left( {\frac{z}
{{f(z)}}} \right)^{\mu + 1} - 1} \right| < \lambda ,\left| z \right| < 1.
相似文献
10.
E. G. Goluzina 《Journal of Mathematical Sciences》2008,150(3):2005-2012
The paper studies the regions of values of the systems {f(z1), f(r1), f(r2),…, f(rn)} and {f(r1), f(r2),…, f (rn)}, where n 2; z1 is an arbitrary fixed point of the disk U = {z: |z| < 1} with Im z1 ≠ 0; rj are fixed numbers, 0 < rj < 1, j = 1, 2,…, n; f ∈ T, and the class T consists of the functions f(z), f(0) = 0, f′(0) = 1, regular in the disk U and
satisfying the condition Im f(z) · Imz > 0 for Im z ≠ 0. As an implication, the region of values of f(z1) in the subclass of functions f ∈ T with prescribed values f(rj) (j = 1, 2,…, n) is determined. Bibliography: 12 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 350, 2007, pp. 5–16. 相似文献
11.
E. G. Goluzina 《Journal of Mathematical Sciences》2007,143(3):3023-3029
The paper studies the region of values Dm,n(T) of the system {f(z1), f(z2),..., f(zm), f(r1), f(r2),..., f(rn)}, where m ≥ 1; n > 1; zj, j = 1, ... m, are arbitrary fixed points of the disk U = {z: |z| < 1} with Im zj ≠ 0, j = 1, 2, ..., m; rj, 0 < rj < 1, j = 1, 2, ..., n, are fixed; f ∈ T, and the class T consists of functions f(z) = z + c2z2 + ... regular in the disk U and satisfying the condition Im f(z) · Im z > 0 for Im z ≠= 0, z ∈ U. An algebraic characterization of the set Dm,n(T) in terms of nonnegative-definite Hermitian forms is provided, and all the boundary functions are described. As an implication,
the region of values of f(z1) in the subclass of functions f ∈ T with prescribed values f(rj) (j = 1, 2, 3) is determined. Bibliography: 12 titles.
Dedicated to the 100th anniversary of my father’s birthday
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 337, 2006, pp. 23–34. 相似文献
12.
Let f be a twice continuously differentiable self-mapping of a unit disk satisfying Poisson differential inequality |△f(z)|≤B·|Df(z)|2 for some B>0 and f(0)= 0.... 相似文献
13.
In this paper we consider special elements of the Fock space #x2131;
n
. That is the space of entire functionsf:ℂ:
n
→ℂ, such that the followingL
2- condition is satisfied:
. Here we show that there exists an entire functiong:ℂ
n
→ℂ such that for every one-dimensional subspace Π⊂ℂ
n
and for all 0<∈<2 we have
, but in the limit case ∈=0 we have
. This result is analogue to a result from [1]. There holomorphic functions on the unit-ball are investigated. Furthermore
the proof — as the one in [1] — uses a theorem from [2]. Therefore we give another application of the results from [2] — namely
for spaces of entire functions. 相似文献
14.
15.
Bloch型函数的高阶径向导数 总被引:1,自引:0,他引:1
讨论了复超球上全纯函数的高阶导数的增长速度 ,证明了f∈Bα 的充分必要条件是supa∈B(1- |z|2 ) m+α- 1|Rmf(z) | <∞ ,或supa∈B∫B(1-|z|2 ) (m+α- 1) |Rmf(z) |pJRφα(z)dv(z) <∞ ,或 (1- |z|2 ) p(m+α- 1) |Rmf(z) |pdv(z)是Bergman Carleson测度 . 相似文献
16.
A. I. Pavlov 《Mathematical Notes》1999,66(4):442-450
The main result of the paper is as follows.Theorem. Suppose that G(z) is an entire function satisfying the following conditions: 1) the Taylor coefficients of the function
G(z) are nonnegative: 2) for some fixed C>0 and A>0 and for |z|>R0, the following inequality holds:
17.
<正> 1.如果函數f(z)在包含實軸土某一區間的區域B中是正則的,f(z)在此實軸區間上取實值.在區域B的其餘地方f(z)與(z)同符號;即 相似文献
18.
Dongsheng Liu 《大学数学》1999,(1)
1IntroductionLetBbetheopenunitbalinCnandSbeitsboundary.LetσbetherotationinvariantprobabilitymeasureonS.Forζ∈Sandδ>0,letQ(ζ,δ)... 相似文献
19.
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