Order convexity and concavity of Lorentz spaces Λp,w, 0 < p < ∞
Abstract
We study order convexity and concavity of quasi-Banach Lorentz spaces Λp,w, where 0 < p < ∞ and w is a locally integrable positive weight function. We show first that Λp,w contains an order isomorphic copy of lp. We then present complete criteria for lattice convexity and concavity as well as for upper and lower estimates for Λp,w. We conclude with a characterization of the type and cotype of Λp,w in the case when Λ p,w is a normable space.
Publication Title
Studia Mathematica
Recommended Citation
Kamińska, A., & Maligranda, L. (2004). Order convexity and concavity of Lorentz spaces Λp,w, 0 < p < ∞. Studia Mathematica, 160 (3), 267-286. https://doi.org/10.4064/sm160-3-5
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