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 Mφf, non-tangential maximal functions M*φf, tangential modification M*φ*,Nf of M*φf and grand maximal functions MFf will be treated with some other maximal functions. And we will compare the Orlicz norms of these maximal functions.
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