Order convexity and concavity of Lorentz spaces
${\mit \Lambda }_{p,w}$, $0 p \infty $
Studia Mathematica, Tome 160 (2004) no. 3, pp. 267-286
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We study order convexity and concavity of quasi-Banach Lorentz spaces ${\mit \Lambda }_{p,w}$, where
$0 p \infty $ and $w$ is a locally integrable positive weight function. We show first that ${\mit \Lambda }_{p,w}$ contains an order isomorphic copy of $l^p$. We then present complete criteria for lattice convexity and concavity as well as for upper and lower estimates for ${\mit \Lambda }_{p,w}$. We conclude with a characterization of the type and cotype of ${\mit \Lambda }_{p,w}$ in the case when ${\mit \Lambda }_{p,w}$ is a normable space.
Keywords:
study order convexity concavity quasi banach lorentz spaces mit lambda where infty locally integrable positive weight function first mit lambda contains order isomorphic copy present complete criteria lattice convexity concavity upper lower estimates mit lambda conclude characterization type cotype mit lambda mit lambda normable space
Affiliations des auteurs :
Anna Kamińska 1 ; Lech Maligranda 2
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title = {Order convexity and concavity of {Lorentz} spaces
${\mit \Lambda }_{p,w}$, $0< p< \infty $},
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${\mit \Lambda }_{p,w}$, $0< p< \infty $
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${\mit \Lambda }_{p,w}$, $0< p< \infty $
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Anna Kamińska; Lech Maligranda. Order convexity and concavity of Lorentz spaces
${\mit \Lambda }_{p,w}$, $0< p< \infty $. Studia Mathematica, Tome 160 (2004) no. 3, pp. 267-286. doi: 10.4064/sm160-3-5
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