We are interested in the widest possible class of Orlicz functions such that the easily calculable quasinorm if and if , on the Orlicz space generated by , is equivalent to the Luxemburg norm . To do this, we use a suitable -condition, lower and upper Simonenko indices and for the generating function , numbers satisfying , and an embedding of into a suitable Köthe function space . We take as the Lebesgue spaces with , when the measure is nonatomic and finite, and the weighted Lebesgue spaces , with and a suitable weight function , when the measure is nonatomic infinite but -finite. We also use condition if and condition if , proving their necessity in most of the considered cases. Our results seem important for applications of Orlicz function spaces.
"Normed Orlicz function spaces which can be quasi-renormed with easily calculable quasinorms." Banach J. Math. Anal. 11 (3) 636 - 660, July 2017. https://doi.org/10.1215/17358787-2017-0009