Monotonicities of Quasi-Normed Orlicz Spaces

Abstract

In this paper, we introduce a new Orlicz function, namely a b-Orlicz function, which is not necessarily convex. The Orlicz spaces LΦ generated by the b-Orlicz function Φ equipped with a Luxemburg quasi-norm contain both classical spaces Lp(p≥1) and Lp(0p1). The Orlicz spaces LΦ 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.

Keywords

• <i>b</i>-Orlicz function
• Orlicz spaces
• quasi-norm
• strict monotonicity
• lower local uniform monotonicity
• upper local uniform monotonicity