ACTA issues

Hardy spaces and multipliers

P├ęter Simon

Acta Sci. Math. (Szeged) 64:1-2(1998), 183-200

Abstract. We consider sublinear operators defined on (dyadic) martingales and give sufficient conditions for them to be bounded from the dyadic Hardy space $ H^p $ to itself. Especially, multiplier operators and their transforms will be considered from $ H^p $ to $ H^p $ for some "powers" $ p $. As a consequence we obtain that for these $ p $'s the space $ H^p $ can be characterized by means of the so-called Sunouchi operator $U$. Namely, a martingale $f$ belongs to $H^p$ ($1/2< p\leq1$, $Sf=0$) if and only if $Uf\in L^p $. Furthermore, $\|f\|_{H^p}\sim\|Uf\|_p $.

AMS Subject Classification (1991): 42C10, 42B15, 43A75, 60G42

Received April 24, 1997 and in revised form September 1, 1997. (Registered under 2655/2009.)