Order convexity and concavity of Lorentz spaces Λp,w, 0 < p < ∞
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.
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