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