Resumen de On the maximal operator associated to a convex body in Rn

María Trinidad Menárguez, Fernando Soria de Diego

• In this paper we study the behaviour of the constants appearing in weak type (1,1) inequalities for the dyadic maximal operator associated to a convex body. We show that for “sufficiently” rapidly increasing sequences these constants are uniformly bounded, independently of dimension and the convex body. From this result we casily recover a theorem of Stein and Strömberg. A simple argument shows that in the case of radial functions, the constants for the full maximal operator are indeed uniformly bounded.