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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
DOI: https://doi.org/10.1090/S0002-9939-01-06109-3
Published electronically: June 6, 2001
MathSciNet review: 1862133
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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.


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

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  • 2. G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, University Press, Cambridge, 1934.
  • 3. Nets Hawk Katz. Matrix valued paraproducts, J. Fourier Anal. Appl. 300 (1997), pp. 913-921. MR 99f:42046
  • 4. F. Nazarov, S. Treil, and A. Volberg, Counterexample to the infinite dimensional Carleson embedding theorem, C.R. Acad. Sci. Paris Sér. I Math., 325 (1997), No.4, pp. 383-388. MR 98d:46039
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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: https://doi.org/10.1090/S0002-9939-01-06109-3
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

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