Transactions of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6850(e) ISSN 0002-9947(p)

Sharp Fourier type and cotype with respect to compact semisimple Lie groups

Author(s): José García-Cuerva; José Manuel Marco; Javier Parcet
Journal: Trans. Amer. Math. Soc. 355 (2003), 3591-3609.
MSC (2000): Primary 43A77; Secondary 22E46, 46L07
Posted: May 15, 2003
MathSciNet review: 1990163
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: Sharp Fourier type and cotype of Lebesgue spaces and Schatten classes with respect to an arbitrary compact semisimple Lie group are investigated. In the process, a local variant of the Hausdorff-Young inequality on such groups is given.

References:

1.: M. E. Andersson, The Hausdorff-Young inequality and Fourier type, Ph.D. Thesis, Uppsala (1993).
2.: K. I. Babenko, An inequality in the theory of Fourier integrals, Izv. Akad. Nauk SSSR 25 (1961), ; English transl., Amer. Math. Soc. Transl. (2) 44 (1965), . MR 25:2379
3.: W. Beckner, Inequalities in Fourier analysis, Ann. of Math. (2) 102 (1975), MR 52:6317
4.: W. Beckner, Pitt's inequality and the uncertainty principle, Proc. Amer. Math. Soc. 123 (1995), MR 95g:42021
5.: E. G. Effros and Z. J. Ruan, Operator Spaces, London Math. Soc. Monogr. 23, Oxford Univ. Press (2000). MR 2002a:46082
6.: G. B. Folland, A Course in Abstract Harmonic Analysis, Stud. Adv. Math., CRC Press (1995). MR 98c:43001
7.: W. Fulton and J. Harris, Representation Theory: A First Course, Graduate Texts in Math., Springer-Verlag, New York, 1991. MR 93a:20069
8.: J. García-Cuerva and J. Parcet, Vector-valued Hausdorff-Young inequality on compact groups, Submitted for publication.
9.: J. García-Cuerva and J. Parcet, Quantized orthonormal systems: A non-commutative Kwapien theorem, Studia Math. 155 (2003),
10.: R. A. Kunze, Fourier transforms on locally compact unimodular groups, Trans. Amer. Math. Soc. 89 (1958), MR 20:6668
11.: G. Pisier, The Operator Hilbert Space OH, Complex Interpolation and Tensor Norms, Mem. Amer. Math. Soc. 122 (1996), No. 585. MR 97a:46024
12.: G. Pisier, Non-commutative vector valued -spaces and completely -summing maps, Astérisque (Soc. Math. France) 247 (1998). MR 2000a:46108
13.: B. Russo, The norm of the $L\sp{p}$ -Fourier transform on unimodular groups, Trans. Amer. Math. Soc. 192 (1974), MR 55:8689a
14.: B. Simon, Representations of Finite and Compact Groups, Graduate Stud. Math. 10, Amer. Math. Soc., Providence, RI, 1996. MR 97c:22001
15.: P. Sjölin, A remark on the Hausdorff-Young inequality, Proc. Amer. Math. Soc. 123 (1995), MR 95m:42007

Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 43A77, 22E46, 46L07

Retrieve articles in all Journals with MSC (2000): 43A77, 22E46, 46L07

Additional Information:

José García-Cuerva
Affiliation: Department of Mathematics, Universidad Autónoma de Madrid, Madrid 28049, Spain
Email: jose.garcia-cuerva@uam.es

José Manuel Marco
Affiliation: Department of Mathematics, Universidad Autónoma de Madrid, Madrid 28049, Spain

Javier Parcet
Affiliation: Department of Mathematics, Universidad Autónoma de Madrid, Madrid 28049, Spain
Email: javier.parcet@uam.es

DOI: 10.1090/S0002-9947-03-03139-8
PII: S 0002-9947(03)03139-8
Keywords: Sharp Fourier type and cotype, Fourier transform, operator space, compact semisimple Lie group, central function, local Hausdorff-Young inequality
Received by editor(s): March 22, 2002
Posted: May 15, 2003
Additional Notes: Research supported in part by the European Commission via the TMR Network ``Harmonic Analysis'' and by Project BFM 2001/0189, Spain
Copyright of article: Copyright 2003, American Mathematical Society

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|