Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. Joseph A. Cima and Alec Matheson, Completely continuous composition operators, Trans. Amer. Math. Soc. 344 (1994), 849-856. MR 94m:47061
  • 2. Carl Cowen and Barbara MacCluer, Composition operators on spaces of analytic functions, CRC Press, Boca Raton, 1995. MR 97i:47056
  • 3. N. Dunford and J. T. Schwartz, Linear Operators, part I, Wiley (Interscience), New York, 1958. MR 22:8302
  • 4. L. Hörmander, $L^{p}$ estimates for (pluri-)subharmonic functions, Math. Scand. 20 (1967), 65-78. MR 38:2323
  • 5. Steven G. Krantz, Function theory of several complex variables, 2nd. ed., Wadsworth, Belmont, 1992. MR 93c:32001
  • 6. B. D. MacCluer, Compact composition operators on $H^{p}(B_{N})$, Michigan Math. J. 32 (1985), 237-248. MR 86g:47037
  • 7. Walter Rudin, New constructions of functions holomorphic in the unit ball of ${\mathbb{C}}^{n}$, CBMS number 63, Amercian Mathematical Society, Providence, 1986. MR 87f:32013

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 42B30

Retrieve articles in all journals with MSC (1991): 42B30

Additional Information

A. Matheson
Affiliation: Department of Mathematics, Lamar University, Beaumont, Texas 77710

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