On the maximal operator associated to a convex body in Rn

• Autores: María Trinidad Menárguez, Fernando Soria de Diego
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 43, Fasc. 3, 1992, págs. 243-251
• Idioma: inglés
• Títulos paralelos:
  • Sobre el operador maximal asociado a un cuerpo convexo n-dimensional
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• Resumen

  • 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.