R. Kerman

The Hardy averaging operator between Orlicz spaces and a new gauge functional characterizing a given Orlicz space

We prove that the largest Orlicz space into which the Hardy averaging operator maps coincides with the largest rearrangement-invariant (r.i.) space mapping into that space; in other words, the optimal Orlicz domain is automatically the optimal r.i.\ domain. More generally, we show that every Luxemburg--Orlicz norm is e...