Comparison between the Orlicz Norms of the Maximal Functions Characterizing the Hardy Spaces

Abstract

In order to characterize the Hardy spaces on an n-dimensional Euclidean space, several maximal functions have been introduced and studied until recently. Among them, vertical maximal functions M_φf, non-tangential maximal functions M^*_φf, tangential modification M^*_φ^*,Nf of M^*_φf and grand maximal functions M_Ff will be treated with some other maximal functions. And we will compare the Orlicz norms of these maximal functions.