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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Dunford-Pettis composition operators
on $H^{1}$ in several variables


Author: A. Matheson
Journal: Proc. Amer. Math. Soc. 126 (1998), 2061-2063
MSC (1991): Primary 42B30
MathSciNet review: 1443394
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Abstract: A bounded composition operator $C_{\phi }$ on $H^{1}(B)$, where $B$ is the unit ball in ${\mathbb{C}}^{n}$, is Dunford-Pettis if and only if the radial limit function $\phi ^{*}$ of $\phi $ takes values on the unit sphere $S$ only on a set of surface measure zero. A similar theorem holds on bounded strongly pseudoconvex domains with smooth boundary.


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Additional Information

A. Matheson
Affiliation: Department of Mathematics, Lamar University, Beaumont, Texas 77710
Email: matheson@math.lamar.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04293-2
PII: S 0002-9939(98)04293-2
Keywords: Dunford-Pettis operator, completely continuous operator, composition operator, Hardy space, inner function, strongly pseudoconvex domain
Received by editor(s): November 15, 1996
Received by editor(s) in revised form: December 27, 1996
Additional Notes: The author was supported in part by NSF grant DMS-9500835.
Communicated by: Dale Alspach
Article copyright: © Copyright 1998 American Mathematical Society