共查询到10条相似文献,搜索用时 140 毫秒
1.
We study interpolating sequences in the unit ball for A–pwith p > 0, the Banach space of holomorphic functions f with(1 – |z|2)p |f(z)| bounded. The finite unions of A–p-interpolatingsequences are characterized by a Carleson type condition. 相似文献
2.
Let B be the space of locally schlicht Bloch functions f whichare analytic in the unit disc with f(0) = f'(0) 1 =0 satisfying 0 < |f'(z)|(1 |z|2) 1. For each fixedz0 we shall determine the shape of the set {logf'(z0): fB},that is, we shall give the sharp distortion estimate for locallyschilcht Bloch functions. 相似文献
3.
For s>0, let Qs be the space of all analytic functions onthe unit disc such that |f'(z)|2(1–|z|2)s dA(z) isan s-Carleson measure. Here we prove that the corona theoremholds for the algebra of pointwise multipliers of Qs. 相似文献
4.
Harmonic Analogues of G. R. Maclane's Universal Functions 总被引:1,自引:0,他引:1
Let E denote the space of all entire functions, equipped withthe topology of local uniform convergence (the compact-opentopology). MacLane [15] constructed an entire function f whosesequence of derivatives (f, f', f', ...) is dense in E; hisconstruction is succinctly presented in a much later note byBlair and Rubel [2], who unwittingly rederived it (see also[3]). We shall call such a function f a universal entire function.In this note we show that analogous universal functions existin the space HN of functions harmonic on RN, where N2. We alsostudy the permissible growth rates of universal functions inHN and show that the set of all such functions is very large. For purposes of comparison, we first review relevant facts aboutuniversal entire functions. The function constructed by MacLaneis of exponential type 1. Duyos Ruiz [7] observed that a universalentire function cannot be of exponential type less than 1. G.Herzog [11] refined MacLane's growth estimate by proving theexistence of a universal entire function f such that |f(z)|=O(rer)as |z|=r. Finally, GrosseErdmann [10] proved the followingsharp result. 相似文献
5.
In this article, we establish distortion theorems for some various subfamilies of Bloch mappings defined in the unit polydisc Dn with critical points, which extend the results of Liu and Minda to higher dimensions. We obtain lower bounds of |det (f'(z))| and ? det (f'(z)) for Bloch mapping f. As an application, some lower and upper bounds of Bloch constants for the subfamilies of holomorphic mappings are given. 相似文献
6.
Let f be an orientation-preserving univalent harmonic mappingof the unit disk U. Then , where h and g are analytic in U. Furthermore, f satisfies theequation
in U, where a(z)=g'(z)/h'(z), and |a(z)| < 1 in U. The functiona(z) is the analytic dilatation of f. In [2], Hengartner and Schober proved the following versionof the Riemann mapping theorem for univalent harmonic mappings.1991 Mathematics Subject Classification 31A05, 31A20. 相似文献
7.
The topological disc (De Paepe's)
isshown here to have non-trivial polynomially convex hull. Infact, the authors show that this holds for all discs of theform , where f is holomorphicon |z|r, and f(z=z2+a3z3+..., with all coefficients an real,and at least one a2n+1 0. 2000 Mathematics Subject Classification32E20. 相似文献
8.
Magdalena Sobczak-Kneć Katarzyna Trąbka-Więcław 《Czechoslovak Mathematical Journal》2011,61(3):733-742
Let T be the family of all typically real functions, i.e. functions that are analytic in the unit disk Δ:= {z ∈ ℂ: |z| < 1}, normalized by f(0) = f′(0) − 1 = 0 and such that Imz Im f(z) ⩾ 0 for z ∈ Δ. 相似文献
9.
Bappaditya Bhowmik Saminathan Ponnusamy Karl-Joachim Wirths 《Monatshefte für Mathematik》2010,29(4):59-75
Let Co(α) denote the class of concave univalent functions in the unit disk
\mathbbD{\mathbb{D}}. Each function f ? Co(a){f\in Co(\alpha)} maps the unit disk
\mathbbD{\mathbb{D}} onto the complement of an unbounded convex set. In this paper we find the exact disk of variability for the functional (1-|z|2)( f¢¢(z)/f¢(z)), f ? Co(a){(1-|z|^2)\left ( f^{\prime\prime}(z)/f^{\prime}(z)\right), f\in Co(\alpha)}. In particular, this gives sharp upper and lower estimates for the pre-Schwarzian norm of concave univalent functions. Next
we obtain the set of variability of the functional (1-|z|2)(f¢¢(z)/f¢(z)), f ? Co(a){(1-|z|^2)\left(f^{\prime\prime}(z)/f^{\prime}(z)\right), f\in Co(\alpha)} whenever f′′(0) is fixed. We also give a characterization for concave functions in terms of Hadamard convolution. In addition to sharp
coefficient inequalities, we prove that functions in Co(α) belong to the H
p
space for p < 1/α. 相似文献
10.
彭志刚 《数学物理学报(A辑)》2008,28(5):945-957
设 H 是一个Hilbert空间. B(H) 表示所有H 到 H 的有界线性算子构成的Banach空间. 设 T= {f(z): f(z)=zI-∑∞n=2 znAn 在单位圆盘|z|<1上解析, 其中系数An是 H 到 H 的紧正Hermitian算子, I 表示 H 上的恒等算子, ∑∞n=2 n(An x, x) ≤1 对所有x ∈H, ∣|x∣∣=1 成立. 该文研究了函数族 T 的极值点. 相似文献