Comparison of Orlicz-Lorentz spaces

Details Comparison of Orlicz-Lorentz spaces Comparison of Orlicz-Lorentz spaces

1991-01-02

arxiv.org/abs/math/9201221v2

Stud. Math. 103 (2), (1992), 161-189

Mathematics

Functional Analysis

Scientific paper

Orlicz-Lorentz spaces provide a common generalization of Orlicz spaces and Lorentz spaces. They have been studied by many authors, including Masty\l o, Maligranda, and Kami\'nska. In this paper, we consider the problem of comparing the Orlicz-Lorentz norms, and establish necessary and sufficient conditions for them to be equivalent. As a corollary, we give necessary and sufficient conditions for a Lorentz-Sharpley space to be equivalent to an Orlicz space, extending results of Lorentz and Raynaud. We also give an example of a rearrangement invariant space that is not an Orlicz-Lorentz space.

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