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Equivalent Characterizations of α-Bloch Functions on the Unit Ball

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Acta Mathematica Sinica,English Series 2011年第12期27卷 2395-2408页

作者： Min Zhu ZHANG Huai Hui CHEN Department of Mathematics Southeast University Nanjing 210096 P. R. China Department of Mathematics Nanjing Normal University Nanjing 210097 P. R. China

In this paper we establish equivalent characterizations of α-Bloch functions on the unit ball without use of derivative, which generalize and improve the results of Nowak, Zhao, Wulan and Li.

关键词： α-Bloch function unit ball Bergman metric

The Schwarz-Pick lemma and Julia lemma for real planar harmonic mappings

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Science China Mathematics 2013年第11期56卷 2327-2334页

作者： CHEN HuaiHui Department of Mathematics Nanjing Normal University

The classical Schwarz-Pick lemma and Julia lemma for holomorphic mappings on the unit disk D are generalized to real harmonic mappings of the unit disk, and the results are precise. It is proved that for a harmonic mapping U of D into the open interval I = （-1, 1）, AU（z）/cosU（z）π/2≤4/π 1/1-｜z｜^2 holds for z E D, where Au（z） is the maximum dilation of U at z. The inequality is sharp for any z E D and any value of U（z）, and the equality occurs for some point in D if and only if U（z） = 4Re {arctan ~a（z）}, z E D, with a M＆bius transformation φa of D onto itself.

关键词： harmonic mappings Schwarz-Pick lemma Julia lemma

On invariant function spaces H_(Q_p)~q(R)

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Science China Mathematics 2013年第10期56卷 1999-2006页

作者： CHEN HuaiHui AULASKARI Rauno Department of Mathematics Nanjing Normal University Department of Physics and Mathematics University of Eastern Finland

New function spaces,which generalize the classical Dirichlet space,BMOA or also the recently defined Qpspace,are introduced on Riemann *** inclusions between these generalized spaces it is shown that the capacity Bloc... 详细信息

关键词： Riemann surface Green's function invariant function space

A SCHWARZ LEMMA FOR HARMONIC FUNCTIONS IN THE REAL UNIT BALL

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Acta Mathematica Scientia 2019年第5期39卷 1339-1344页

作者： Shaoyu DAI Huaihui CHEN School of Mathematics Southeast University Nanjing 210096 China Department of Mathematics Jinling Institute of Technology Nanjing 211169 China Department of Mathematics Nanjing Normal University Nanjing 210097 China

We establish a precise Schwarz lemma for real-valued and bounded harmonic functions in the real unit ball of dimension n. This extends Chen's Schwarz-Pick lemma for real-valued and bounded planar harmonic mapping.

关键词： harmonic functions Schwarz-Pick lemma unit ball

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分担值与具有重零点的亚纯函数正规族

数学学报（中文版） 2013年第3期56卷 343-352页

作者：王品玲刘丹方明亮上海立信会计学院数学与信息学院上海201620 华南农业大学应用数学研究所广州510642

主要证明了:设k≥2是一个正整数,M是一个正数,c是一个非零有穷复数.F是区域D内的一族亚纯函数,其中每个函数的零点的重数至少是k.若对于F中的任意函数f,f(z)=0f^((k))(x)=0,f^((k))(z)=c■|f^((k+1))(z)|≥M,则F在D内正规,其中c≠0是... 详细信息

主要证明了:设k≥2是一个正整数,M是一个正数,c是一个非零有穷复数.F是区域D内的一族亚纯函数,其中每个函数的零点的重数至少是k.若对于F中的任意函数f,f(z)=0f^((k))(x)=0,f^((k))(z)=c■|f^((k+1))(z)|≥M,则F在D内正规,其中c≠0是必需的.

关键词：亚纯函数分担值正规族