Paley's inequality for nonabelian groups
ChianYeong Chuah, Yazhou Han, Zhenchuan Liu, and Tao Mei
TL;DR
This paper extends Paley's inequality to nonabelian discrete groups, unifying previous results for abelian groups and operator-valued functions, and introduces new examples of Paley sequences and a0(p) sets on free groups.
Contribution
It generalizes Paley's inequality to nonabelian groups, unifies existing theories, and provides new examples of Paley sequences and a0(p) sets.
Findings
Unified Paley's inequality for nonabelian groups
Extended results to operator-valued functions
Constructed new examples on free groups
Abstract
This article studies Paley's theory for lacunary Fourier series on (nonabelian) discrete groups. The results unify and generalize the work of Rudin for abelian discrete groups and the work of Lust-Piquard and Pisier for operator valued functions, and provide new examples of Paley sequences and sets on free groups.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Harmonic Analysis Research · Advanced Banach Space Theory