Theoretical analysis reveals sharp lp-operator norms for spherical averaging operators in Gromov hyperbolic groups, indicating lower bounds for spherical combinatorial expansion.
We obtain asymptotic estimates for the ᵖ-operator norm of spherical averaging operators associated to certain geometric group actions. The motivating example is the case of Gromov hyperbolic groups, for which we obtain asymptotically sharp estimates. We deduce asymptotic lower bounds for the combinatorial expansion of spheres.
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Bogdan Nica (2024) studied this question.
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