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Abstract
We study boundary representations of hyperbolic groups Γ on the (compactly embedded) function space Wlog,2(∂Γ)⊂L2(∂Γ), the domain of the logarithmic Laplacian on ∂Γ. We show that they are not uniformly bounded, and establish their exact growth (up a multiplicative constant): they grow with the square root of the length of g∈Γ. We also obtain Lp--analogue of this result. Our main tool is a logarithmic Sobolev inequality on bounded Ahlfors--David regular metric measure spaces.
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Accepted/In Press date: 12 August 2024
Identifiers
Local EPrints ID: 494939
URI: http://eprints.soton.ac.uk/id/eprint/494939
PURE UUID: 413b06b2-68fa-49b8-80d5-2143177a7707
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Date deposited: 23 Oct 2024 16:54
Last modified: 24 Oct 2024 01:45
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Contributors
Author:
Kevin Boucher
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