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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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


Authors: José García-Cuerva, José Manuel Marco and Javier Parcet
Journal: Trans. Amer. Math. Soc. 355 (2003), 3591-3609
MSC (2000): Primary 43A77; Secondary 22E46, 46L07
Published electronically: May 15, 2003
MathSciNet review: 1990163
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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.


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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: http://dx.doi.org/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
Published electronically: 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
Article copyright: © Copyright 2003 American Mathematical Society