Complex Analysis and Operator Theory

, Volume 6, Issue 5, pp 1025–1036 | Cite as

Landau–Bloch Constants for Functions in α-Bloch Spaces and Hardy Spaces

  • Sh. Chen
  • S. PonnusamyEmail author
  • X. Wang


In this paper, we obtain a sharp distortion theorem for a class of functions in α-Bloch spaces, and as an application of it, we establish the corresponding Landau’s theorem. These results generalize the corresponding results of Bonk, Minda and Yanagihara, and Liu, respectively. We also prove the existence of Landau–Bloch constant for a class of functions in Hardy spaces and the obtained result is a generalization of the corresponding result of Chen and Gauthier.


Landau–Bloch constant Holomorphic function α-Bloch space Hardy space 

Mathematics Subject Classification (2000)

Primary 32A10 Secondary 32A17 32A18 32A35 


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© Springer Basel AG 2012

Authors and Affiliations

  1. 1.College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education)Hunan Normal UniversityChangshaPeople’s Republic of China
  2. 2.Department of MathematicsIndian Institute of Technology MadrasChennaiIndia

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