Order convexity and concavity of Lorentz spaces ${\mit \Lambda }_{p,w}$, $0 p \infty $

Anna Kamińska ¹   ; Lech Maligranda ²

¹ Department of Mathematical Sciences The University of Memphis Memphis, TN 38152, U.S.A.
² Department of Mathematics Lule{\accent 23 a} University of Technology SE-971 87 Lule{\accent 23 a}, Sweden

Studia Mathematica, Tome 160 (2004) no. 3, pp. 267-286

Résumé

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.

Détail

DOI : 10.4064/sm160-3-5

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