Dunford-Pettis composition operators on $H^1$ in several variables
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- by A. Matheson PDF
- Proc. Amer. Math. Soc. 126 (1998), 2061-2063 Request permission
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.References
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Additional Information
- A. Matheson
- Affiliation: Department of Mathematics, Lamar University, Beaumont, Texas 77710
- Email: matheson@math.lamar.edu
- 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
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2061-2063
- MSC (1991): Primary 42B30
- DOI: https://doi.org/10.1090/S0002-9939-98-04293-2
- MathSciNet review: 1443394