Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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ON DUALITY OF WEIGHTED BLOCH SPACES IN ℂn

  • Yang, Gye Tak (Department of Information Security Konyang University) ;
  • Choi, Ki Seong (Department of Information Security Konyang University)
  • Received : 2010.05.20
  • Accepted : 2010.08.12
  • Published : 2010.09.30
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Abstract

In this paper, we consider the weighted Bloch spaces ${\mathcal{B}}_q$(q > 0) on the open unit ball in ${\mathbb{C}}^n$. We prove a certain integral representation theorem that is used to determine the degree of growth of the functions in the space ${\mathcal{B}}_q$ for q > 0. This means that for each q > 0, the Banach dual of $L_a^1$ is ${\mathcal{B}}_q$ and the Banach dual of ${\mathcal{B}}_{q,0}$ is $L_a^1$ for each $q{\geq}1$.

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