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

 

Asymptotic properties of the vector Carleson embedding theorem


Author: Michael Goldberg
Journal: Proc. Amer. Math. Soc. 130 (2002), 529-531
MSC (2000): Primary 42B20, 42A50
Published electronically: June 6, 2001
MathSciNet review: 1862133
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Abstract | References | Similar Articles | Additional Information

Abstract:

The dyadic Carleson embedding operator acting on $\mathbb{C}^n$-valued functions has norm at least $C\log n$. Thus the Carleson Embedding Theorem fails for Hilbert space valued functions.


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Additional Information

Michael Goldberg
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720-3840
Email: mikeg@math.berkeley.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06109-3
PII: S 0002-9939(01)06109-3
Keywords: Carleson embedding theorem, vector valued functions, operator valued measures, weights
Received by editor(s): July 5, 2000
Published electronically: June 6, 2001
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2001 American Mathematical Society