Orlicz spaces for which the Hardy-Littlewood maximal operators is bounded

• Autores: Diego Gallardo
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 32, Nº 2, 1988, págs. 261-266
• Idioma: inglés
• DOI: 10.5565/publmat_32288_09
• Títulos paralelos:
  • Espacios de Orlicz para los que el operador maximal de Hardey-Littlewood es acotado
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• Resumen

  • Let M be the Hardy-Littlewood maximal operator defined by:

    Mf(x) = supx Î Q 1/|Q| ?Q |f| dx, (f Î Lloc(Rn)), where the supreme is taken over all cubes Q containing x and |Q| is the Lebesgue measure of Q. In this paper we characterize the Orlicz spaces Lf*, associated to N-functions f, such that M is bounded in Lf*. We prove that this boundedness is equivalent to the complementary N-function ? of f satisfying the ?2-condition in [0,8), that is, sups>0 ?(2s) / ?(s) < 8.