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Monotonicities of Quasi-Normed Orlicz Spaces
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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(0<p<1). 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.
Title: Monotonicities of Quasi-Normed Orlicz Spaces
Description:
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(0<p<1).
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.
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