Some geometric properties of Lorentz-Orlicz spaces

摘要

A function φ:R_+ → R_+ is said to be a Young's function if 0 is convex, φ(0) = 0, and φ(u) > 0 for all u > 0. If (j) is a Young's function, then the complementary function ψ: R_+ → R_+ ∪ {∞} m t/ie sense of Young to φ is the function defined by ψ(u) = sup_(v>0) {uv - φ (v)} for all u ∈ R_+.