Acta mathematica scientia,Series B

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COMPOSITION OPERATORS ON THE LITTLE BLOCH SPACE IN POLYDISCS

 ZHOU Ze-Hua, SHU Min, SHI Ji-Fu   

  • Online:2005-10-11 Published:2005-10-11
  • Supported by:

    Supported by the National Natural Science Foundation of China (10371091,
    10001030), and LiuHui Center for Applied Mathematics, Nankai University and Tianjin University

Abstract:

Let Un be the unit polydisc of Cn and  = (1, · · · , n) a holomorphic self-
map of Un. This paper shows that the composition operator C induced by  is bounded
on the little Bloch space 0(Un) if and only if l 2 0(Un) for every l = 1, 2, · · · , n,
and also gives a sufficient and necessary condition for the composition operator C to be
compact on the little Bloch space 0(Un).

Key words: Little Bloch space, distinguished boundary, composition operator, Bergman metric

CLC Number: 

  • 32A30
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