Stephen J. Montgomery-Smith
Published 1991-01-02, updated 1999-12-04Version 2
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.
Journal: Stud. Math. 103 (2), (1992), 161-189
The structure of subspaces in Orlicz spaces between $L^1$ and $L^2$
Embeddings of rearrangement invariant spaces that are not strictly singular
A Note on the Completeness of All Translates of a Function in the Orlicz Spaces
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