Acta mathematica scientia,Series B ›› 2000, Vol. 20 ›› Issue (2): 278-288.

• Articles • Previous Articles    

VECTOR-VALUED HOLOMORPHIC FUNCTIONS ON
THE COMPLEX BALL AND THE ANALYTIC
RADON-NIKODYM PROPERTY

 CHEN Ze-Gan, OU Yang-Cai-Heng   

  1. Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China
  • Online:2000-04-18 Published:2000-04-18
  • Supported by:

    Project supported by the National Natural Science Foundation of China
    (No:19771082)

Abstract:

The complex Banach spaces X with values in which every bounded holomorphic
function in the unit ball B of Cd(d > 1) has boundary limits almost surely are exactly
the spaces with the analytic Radon-Nikodym property.The proof is based on inner Hardy
martingales introduced here. The inner Hardy martingales are constructed in terms of
inner functions in B and are reasonable discrete approximations for the image processes
of the holomorphic Brownian motion under X-valued holomorphic functions in B.

Key words: Complex Banach spaces, the analytic Radon-Nikodym property, inner functions,
inner Hardy martingales

CLC Number: 

  • 46B20
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