Asymptotic properties of the vector Carleson embedding theorem
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- by Michael Goldberg
- Proc. Amer. Math. Soc. 130 (2002), 529-531
- DOI: https://doi.org/10.1090/S0002-9939-01-06109-3
- Published electronically: June 6, 2001
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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
- John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
- G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, University Press, Cambridge, 1934.
- Lawrence M. Graves, The Weierstrass condition for multiple integral variation problems, Duke Math. J. 5 (1939), 656–660. MR 99
- Fedor Nazarov, Serguei Treil, and Alexander Volberg, Counterexample to the infinite-dimensional Carleson embedding theorem, C. R. Acad. Sci. Paris Sér. I Math. 325 (1997), no. 4, 383–388 (English, with English and French summaries). MR 1467091, DOI 10.1016/S0764-4442(97)85621-2
- F. Nazarov, G. Pisier, S. Treil, and A. Volberg, Sharp estimates in the vector Carleson imbedding theorem and for vector paraproducts, Preprint.
Bibliographic Information
- Michael Goldberg
- Affiliation: Department of Mathematics, University of California, Berkeley, California 94720-3840
- MR Author ID: 674280
- ORCID: 0000-0003-1039-6865
- Email: mikeg@math.berkeley.edu
- Received by editor(s): July 5, 2000
- Published electronically: June 6, 2001
- Communicated by: Christopher D. Sogge
- © Copyright 2001 American Mathematical Society
- 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
- MathSciNet review: 1862133