Monotonicities of Quasi-Normed Orlicz Spaces.

In this paper, we introduce a new Orlicz function, namely a b-Orlicz function, which is not necessarily convex. The Orlicz spaces L Φ generated by the b-Orlicz function Φ equipped with a Luxemburg quasi-norm contain both classical spaces L p (p ≥ 1) and L p (0 < p < 1) . The Orlicz spaces L Φ are quasi-Banach spaces. Some basic properties in quasi-normed Orlicz spaces are discussed, and the criteria that a quasi-normed Orlicz space is strictly monotonic and lower (upper) locally uniformly monotonic are given. [ABSTRACT FROM AUTHOR]