Menárguez, M. Trinidad; Soria, Fernando On the maximal operator associated to a convex body in \(\mathbb{R}^ n\). (English) Zbl 0792.42007 Collect. Math. 43, No. 3, 243-251 (1992). 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. Reviewer: S.G.Krantz (St.Louis) Cited in 6 Documents MSC: 42B25 Maximal functions, Littlewood-Paley theory 52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces) Keywords:convex bodies; maximal operators of Hardy-Littlewood type; \(n\log n\) operators; weak type estimates PDFBibTeX XMLCite \textit{M. T. Menárguez} and \textit{F. Soria}, Collect. Math. 43, No. 3, 243--251 (1992; Zbl 0792.42007) Full Text: EuDML