All radial log-concave maximal function L^p norms converge to a universal limit λ(p) as dimension→∞, with the Euclidean ball asymptotically extremal.
Stein, and Błażej Wróbel,On the Hardy-Littlewood maximal functions in high dimensions: continuous and discrete perspective, Geometric aspects of harmonic analysis, 2021, pp
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High-dimensional limits and extremizers for maximal functions associated with log-concave densities
All radial log-concave maximal function L^p norms converge to a universal limit λ(p) as dimension→∞, with the Euclidean ball asymptotically extremal.