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On the maximal operator associated to a convex body in \(\mathbb{R}^ n\). (English) Zbl 0792.42007

In recent years there has been considerable interest in the study of the independence of dimension for estimates for certain maximal operators of Hardy-Littlewood type. The present paper presents a unified approach to such questions, showing as it does that there is a collection of \(n\log n\) operators, satisfying weak type estimates that are independent of dimension, that controls all the standard maximal operators.

MSC:

42B25 Maximal functions, Littlewood-Paley theory
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
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