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Vector valued Fourier analysis on unimodular groups

✍ Scribed by Hun Hee Lee

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 257 KB
Volume: 279
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200310399

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✦ Synopsis

Abstract

The notion of Fourier type and cotype of linear maps between operator spaces with respect to certain unimodular (possibly nonabelian and noncompact) group is defined here. We develop analogous theory compared to Fourier types with respect to locally compact abelian groups of operators between Banach spaces. We consider the Heisenberg group as an example of nonabelian and noncompact groups and prove that Fourier type and cotype with respect to the Heisenberg group implies Fourier type with respect to classical abelian groups. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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