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arXiv · 2408.10949

Cotlar Properties, Hyperbolicity, and Unconditional Fourier Decompositions

Tao Mei
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Abstract

Let a discrete group $\Gamma$ act by isometries on a metric space $X$. We show that actions on geodesic hyperbolic spaces satisfy a branch Cotlar property. Under a finite low-orbit-frequency hypothesis, this yields uniform $L^4$-unconditionality for branch subspaces associated with sufficiently separated subsets; when the union of these branches has finite complement, the corresponding signed projections are uniformly bounded on $L^p(\widehat\Gamma)$ for every $1<p<\infty$. Finally, for connected vertex-transitive graphs, we prove that a scale-wise branch Cotlar property characterizes hyperbolicity of $X$.

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Tao Mei. 2024-08-20. Cotlar Properties, Hyperbolicity, and Unconditional Fourier Decompositions. https://arxiv.org/abs/2408.10949

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