On vector-valued inequalities for Sidon sets and sets of interpolation

DOI10.4064/CM-64-2-233-244zbMATH Open0838.43007arXivmath/9209216OpenAlexW1605575139MaRDI QIDQ4322363

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Publication date: 17 July 1995

Published in: Colloquium Mathematicum (Search for Journal in Brave)

Abstract: Let $E$ be a Sidon subset of the integers and suppose $X$ is a Banach space. Then Pisier has shown that $E$-spectral polynomials with values in $X$ behave like Rademacher sums with respect to $L_p-$norms. We consider the situation when $X$ is a quasi-Banach space. For general quasi-Banach spaces we show that a similar result holds if and only if $E$ is a set of interpolation ($I_0$-set). However for certain special classes of quasi-Banach spaces we are able to prove such a result for larger sets. Thus if $X$ is restricted to be ``natural then the result holds for all Sidon sets. We also consider spaces with plurisubharmonic norms and introduce the class of analytic Sidon sets.

Full work available at URL: https://arxiv.org/abs/math/9209216

zbMATH Keywords

Banach spacequasi-Banach spaceBorel functionsRademacher functionSidon setquasinormcompact Abelian groupnon-locally convex spacesset of interpolation

Mathematics Subject Classification ID

Special sets (thin sets, Kronecker sets, Helson sets, Ditkin sets, Sidon sets, etc.) (43A46)

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