Paley's Theory for Lacunary Fourier Series on Discrete Groups: a Semigroup-Interpretation

Abstract

The main result is a Paley's theory for lacunary Fourier series using semigroup-BMO and $H^1$ spaces. This interpretation allows an extension of Paley's theory to general discrete groups, complementing the work of Rudin for abelian groups with a total order, and Lust-Piquard and Pisier's work for lacunary Fourier series with operator-valued coefficients.

9 pages

References in corpus (1)

• Subgaussian sequences in probability and Fourier analysis

Cited by in corpus (1)

• BMO spaces of $\sigma$-finite von Neumann algebras and Fourier-Schur multipliers on $S{U}_q(2)$