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Type norms with respect to characters of compact abelian groups and algebraic relations

✍ Scribed by Aicke Hinrichs

Publisher: Springer
Year: 1997
Tongue: English
Weight: 392 KB
Volume: 68
Category: Article
ISSN: 0003-889X
DOI: 10.1007/s000130050056

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## Abstract A linear and bounded operator __T__ between Banach spaces __X__ and __Y__ has Fourier type 2 with respect to a locally compact abelian group __G__ if there exists a constant __c__ > 0 such that∥__T__$\hat f$∥~2~ ≤ __c__∥__f__∥~2~ holds for all __X__‐valued functions __f__ ∈ __L__^__X__^

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