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COMPOSITION OPERATORS ON THE PRIVALOV SPACES OF THE UNIT BALL OF ℂn
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 Title & Authors
COMPOSITION OPERATORS ON THE PRIVALOV SPACES OF THE UNIT BALL OF ℂn
UEKI SEI-ICHIRO;
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 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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2.
Weighted composition operators from Bergman–Privalov-type spaces to weighted-type spaces on the unit ball, Applied Mathematics and Computation, 2010, 217, 5, 1939  crossref(new windwow)
3.
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Composition Operators from the Weighted Bergman Space to the th Weighted Spaces on the Unit Disc, Discrete Dynamics in Nature and Society, 2009, 2009, 1  crossref(new windwow)
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Composition followed by differentiation from H∞ and the Bloch space to nth weighted-type spaces on the unit disk, Applied Mathematics and Computation, 2010, 216, 12, 3450  crossref(new windwow)
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On the Generalized Hardy Spaces, Abstract and Applied Analysis, 2010, 2010, 1  crossref(new windwow)
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On operator from the logarithmic Bloch-type space to the mixed-norm space on the unit ball, Applied Mathematics and Computation, 2010, 215, 12, 4248  crossref(new windwow)
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Products of composition and differentiation operators from Zygmund spaces to Bloch spaces and Bers spaces, Applied Mathematics and Computation, 2010, 217, 7, 3144  crossref(new windwow)
10.
Norms of some operators on bounded symmetric domains, Applied Mathematics and Computation, 2010, 216, 1, 187  crossref(new windwow)
11.
Weighted differentiation composition operators from H∞ and Bloch spaces to nth weighted-type spaces on the unit disk, Applied Mathematics and Computation, 2010, 216, 12, 3634  crossref(new windwow)
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