All radial log-concave maximal function L^p norms converge to a universal limit λ(p) as dimension→∞, with the Euclidean ball asymptotically extremal.
Picardello (ed.), Trends in Harmonic Analysis, Springer INdAM Series 3, 2013
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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.