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

 

Leibenzon's backward shift and composition operators


Author: Evgueni Doubtsov
Journal: Proc. Amer. Math. Soc. 129 (2001), 3495-3499
MSC (2000): Primary 47B38
Published electronically: July 10, 2001
MathSciNet review: 1860481
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Abstract:

We apply Leibenzon's backward shift to show that the composition operator on the unit ball of $\mathbb{C}^n$ always maps the weighted Hardy space $H^2_{1-n}$ into the Hardy class $H^2$.


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Additional Information

Evgueni Doubtsov
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Address at time of publication: ul. Partizana Germana 14/117, kv. 335, 198205 St. Petersburg, Russia
Email: ed@ED8307.spb.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06325-0
PII: S 0002-9939(01)06325-0
Keywords: Composition operator, Leibenzon's backward shift
Received by editor(s): March 1, 1999
Published electronically: July 10, 2001
Communicated by: David R. Larson
Article copyright: © Copyright 2001 American Mathematical Society