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Asymptotic properties of the vector Carleson embedding theorem
Author(s):
Michael
Goldberg
Journal:
Proc. Amer. Math. Soc.
130
(2002),
529-531.
MSC (2000):
Primary 42B20, 42A50
Posted:
June 6, 2001
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Abstract:
The dyadic Carleson embedding operator acting on  -valued functions has norm at least  . Thus the Carleson Embedding Theorem fails for Hilbert space valued functions.
References:
-
- 1.
- J. B. Garnett, Bounded Analytic Functions, Acad. Press, New York, 1981. MR 83g:30037
- 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
- 5.
- F. Nazarov, G. Pisier, S. Treil, and A. Volberg, Sharp estimates in the vector Carleson imbedding theorem and for vector paraproducts, Preprint.
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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:
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
Posted:
June 6, 2001
Communicated by:
Christopher D. Sogge
Copyright of article:
Copyright
2001,
American Mathematical Society
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