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arXiv · 2606.19880

A Riesz-Thorin Approach to the Rapid Decay Property for Free Groups

Guillaume Delord
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Abstract

We establish $L^p$ bounds for operators associated with the quasi-regular representation of the free group on its Gromov boundary. The $p=2$ case recovers Haagerup's inequality, yielding a new interpolation-theoretic proof of the the Rapid Decay property for the free group.

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Guillaume Delord. 2026-06-18. A Riesz-Thorin Approach to the Rapid Decay Property for Free Groups. https://arxiv.org/abs/2606.19880

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