We study order convexity and concavity of quasi-Banach Lorentz spaces , where 0 < p < ∞ and w is a locally integrable positive weight function. We show first that contains an order isomorphic copy of . We then present complete criteria for lattice convexity and concavity as well as for upper and lower estimates for . We conclude with a characterization of the type and cotype of in the case when is a normable space.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm160-3-5,
author = {Anna Kami\'nska and Lech Maligranda},
title = {Order convexity and concavity of Lorentz spaces $$\Lambda$\_{p,w}$, 0 < p < $\infty$},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {267-286},
zbl = {1057.46026},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm160-3-5}
}
Anna Kamińska; Lech Maligranda. Order convexity and concavity of Lorentz spaces $Λ_{p,w}$, 0 < p < ∞. Studia Mathematica, Tome 162 (2004) pp. 267-286. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm160-3-5/