COMPOSITION OPERATORS ON THE PRIVALOV SPACES OF THE UNIT BALL OF ℂ^{n}

- Journal title : Journal of the Korean Mathematical Society
- Volume 42, Issue 1, 2005, pp.111-127
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2005.42.1.111

Title & Authors

COMPOSITION OPERATORS ON THE PRIVALOV SPACES OF THE UNIT BALL OF ℂ^{n}

UEKI SEI-ICHIRO;

UEKI SEI-ICHIRO;

Abstract

Let B and S be the unit ball and the unit sphere in , respectively. Let be the normalized Lebesgue measure on S. Define the Privalov spaces $N^P(B)\;(1\;<\;p\;<\;{\infty})$ by $$N^P(B)\;=\;\{\;f\;{\in}\;H(B) : \sup_{0 be a holomorphic self-map of B. Let denote the pull-back measure . In this paper, we prove that the composition operator is metrically bounded on (B) if and only if for some constant C and is metrically compact on if and only if as uniformly in . Our results are an analogous results for Mac Cluer's Carleson-measure criterion for the boundedness or compactness of on the Hardy spaces .

Keywords

Hardy spaces;Privalov spaces;composition operators;unit ball of ;

Language

English

Cited by

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