Vector-valued Hausdorff-Young inequality on compact groups

Details Vector-valued Hausdorff-Young inequality on compact groups Vector-valued Hausdorff-Young inequality on compact groups

2003-12-11

arxiv.org/abs/math/0312241v2

Proc. London Math. Soc. 88 (2004), 796-816.

Mathematics

Functional Analysis

To appear in Proc. London. Math. Soc. 30 pages

Scientific paper

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. 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 questions are posed.

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