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Vector-valued Hausdorff–Young inequality on compact groups

Published online by Cambridge University Press:  14 April 2004

J. García-Cuerva  and
J. Parcet
J. García-Cuerva
Affiliation:
Departamento de Matemáticas, C-XV, Universidad Autónoma de Madrid, 28049 Madrid, Spain. E-mail: jose.garcia-cuerva@uam.es
J. Parcet
Affiliation:
Departamento de Matemáticas, C-XV, Universidad Autónoma de Madrid, 28049 Madrid, Spain. E-mail: javier.parcet@uam.es
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Abstract

The main purpose of this paper is to study the validity of the Hausdorff–Young inequality for vector-valued functions defined on a non-commutative compact group. As we explain in the introduction, the natural context for this research is that of operator spaces. This leads us to formulate a whole new theory of Fourier type and cotype for the category of operator spaces. The present paper is the first step in this program, where the basic theory is presented, the main examples are analyzed and some important questions are posed.

Keywords

operator spaceHausdorff–Young inequalitycompact groupFourier type and cotype43A7746L07
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 88 , Issue 3 , May 2004 , pp. 796 - 816
Copyright
2004 London Mathematical Society

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Footnotes

This research was supported in part by the TMR Network ‘Harmonic Analysis’, and in part by Project BFM 2001/0189, Spain.