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SCHWARZ-PICK ESTIMATES FOR BOUNDED holomorphic functions ON CLASSICAL DOMAINS

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Acta Mathematica Scientia 2011年第4期31卷 1377-1382页

作者：刘洋陈志华 Department of Mathematics Zhejiang Normal University Department of Mathematics Tongji University

In this paper, Schwarz-Pick estimates for high order Fr′echet derivatives of bounded holomorphic functions on three kinds of classical domains are presented. We generalize the early work on Schwarz-Pick estimates of ... 详细信息

关键词： Schwarz-Pick estimate holomorphic functions classical domains

SOME REMARKS ON holomorphic functions AND TAYLOR SERIES IN C^n

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Acta Mathematica Scientia 2008年第4期28卷 721-726页

作者：余家荣 School of Mathematics and Statistics Wuhan University

Some previous results on convergence of Taylor series in C^n [3] are improved by indicating outside the domain of convergence the points where the series diverges and simplifying some proofs. These results contain the Cauchy-Hadamard theorem in C. Some Cauchy integral formulas of a holomorphic function on a closed ball in C^n are constructed and the Taylor series expansion is deduced.

关键词： Polar coordinates Taylor series holomorphic functions

Dimension Estimate of Polynomial Growth holomorphic functions

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Peking Mathematical Journal 2021年第2期4卷 187-202页

作者： Gang Liu School of Mathematical Sciences Shanghai Key Laboratory of PMMPEast China Normal UniversityShanghai 200241China

On a complete noncompact Kähler manifold M^(n)(complex dimension)with non-negative Ricci curvature and Euclidean volume growth,we prove that polynomial growth holomorphic functions of degree d has an dimension upper b... 详细信息

关键词： Dimension estimate holomorphic functions Gromov-Hausdorff convergence

WEIGHTED INTEGRALS OF holomorphic functions

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Applied Mathematics(A Journal of Chinese Universities) 2004年第4期19卷 474-480页

作者： HuZhangjian LiuTaishun Dept.ofMath. Univ.ofSci.andTech.ofChinaHefei230026China.

Given an admissible weight w and 0holomorphic functions f in the unit disc D. Here,ψ(r)=∫ 1 rw(t)dtw(r) is t... 详细信息

Given an admissible weight w and 0holomorphic functions f in the unit disc D. Here,ψ(r)=∫ 1 rw(t)dtw(r) is the distortion of w. As an application of the above estimate, it is proved that the Cesàro operator C[·] is bounded on the weighted Bergman spaces L p a,w (D).

关键词： admissible weight holomorphic functions Cesàro operator.

Normal Families of holomorphic functions Concerning Shared a Polynomial

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Chinese Quarterly Journal of Mathematics 2011年第3期26卷 394-399页

作者： LIU Zhi-hong LI Ying-chun HUANG Bin College of Mathematics Honghe University Mengzi 661100 China College of Mathematics and Computing Science Changsha University of Science and Technology Changsha 410076 China

In this paper,we study normal families of holomorphic function concerning shared a *** F be a family of holomorphic functions in a domain D,k(2)be a positive integer,K be a positive number andα(z)be a polynomial of degree p(p 1).For each f∈F and z∈D,if f and f sharedα(z)CM and|f(k)(z)|K whenever f(z)-α(z)=0 in D, then F is normal in D.

关键词： holomorphic functions normal family shared values polynomial

Some Characterizations of the Properties ■~∞ and LB_∞

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Acta Mathematica Sinica,English Series 2004年第4期20卷 613-628页

作者： Thuan Quang THAI Department of Mathematics Pedagogical Institute of Quynhon170 An Duong VuongQuynhonBinhdinhVietnam

The aim of this paper is to give some properties of the linear topological invariant LB^-∞ Using these results we show that a nuclear Fréchet space F has the property LB∞ if and only if every separately holomorphic function on an open subset U × V of E × F^* has a local Dirichlet representation,where E is a nuclear Fréchet space with the property LB^-∞ having a basis.

关键词： holomorphic functions Topological linear invariants Dirichlet representation

A Criterion of Normality Based on a Single holomorphic Function

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Acta Mathematica Sinica,English Series 2011年第1期27卷 141-154页

作者： Xiao Jun LIU Shahar NEVO Department of Mathematics University of Shanghai for Science and Technology Shanghai 200093 P. R. China Department of Mathematics Bar-Ilan University 52900 Ramat-Gan Israel

Let F be a family of functions holomorphic on a domain D C C. Let k ≥ 2 be an integer and let h be a holomorphic function on D, all of whose zeros have multiplicity at most k- 1, such that h（z） has no common zeros with any f∈F. Assume also that the following two conditions hold for every f ∈F ：（a） f（z） = 0 == f （z） = h（z）; and （b） y（z） = h（z） == ｜f（k）（z）｜ ≤ c, where c is a *** F is normal on D.

关键词： Normal family holomorphic functions zero points

holomorphic Connections and Problems of Lifts

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Chinese Annals of Mathematics,Series B 2024年第5期45卷 677-684页

作者： Arif SALIMOV Narmina GURBANOVA Department of Algebra and Geometry Baku State UniversityBakuAzerbaijan

Considering the bundle of 2-jets as a realization of the holomorphic manifold over 3-dimensional nilpotent algebra,the authors introduce a new class of lifts of connections in the bundle of 2-jets which is a generaliz... 详细信息

关键词： holomorphic functions Bundle of 2-jets Deformed lift Pure connection

A PICARD TYPE THEOREM AND BLOCH LAW

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Chinese Annals of Mathematics,Series B 1994年第1期15卷 75-80页

作者： YE YASHENG SHANGHAI INST MECH & ELECT ENGN DEPT MATHSHANGHAI 200093PEOPLES R CHINA

A picard type theorem is proved, and a counterexample is given to show that the Bolch Lawis not true generally.

关键词： Picard type theorem Bloch law holomorphic functions Meromorphic functions.