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

Anna Kamińska, and Lech Maligranda. "Order convexity and concavity of Lorentz spaces $Λ_{p,w}$, 0 < p < ∞." Studia Mathematica 160.3 (2004): 267-286. <http://eudml.org/doc/284451>.

@article{AnnaKamińska2004,
abstract = {We study order convexity and concavity of quasi-Banach Lorentz spaces $Λ_\{p,w\}$, where 0 < p < ∞ and w is a locally integrable positive weight function. We show first that $Λ_\{p,w\}$ 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 $Λ_\{p,w\}$. We conclude with a characterization of the type and cotype of $Λ_\{p,w\}$ in the case when $Λ_\{p,w\}$ is a normable space.},
author = {Anna Kamińska, Lech Maligranda},
journal = {Studia Mathematica},
keywords = {Lorentz spaces; quasi-Banach lattices; rearrangement invariant spaces; normability; Boyd indices; weight; weighted inequalities},
language = {eng},
number = {3},
pages = {267-286},
title = {Order convexity and concavity of Lorentz spaces $Λ_\{p,w\}$, 0 < p < ∞},
url = {http://eudml.org/doc/284451},
volume = {160},
year = {2004},
}

TY - JOUR
AU - Anna Kamińska
AU - Lech Maligranda
TI - Order convexity and concavity of Lorentz spaces $Λ_{p,w}$, 0 < p < ∞
JO - Studia Mathematica
PY - 2004
VL - 160
IS - 3
SP - 267
EP - 286
AB - We study order convexity and concavity of quasi-Banach Lorentz spaces $Λ_{p,w}$, where 0 < p < ∞ and w is a locally integrable positive weight function. We show first that $Λ_{p,w}$ 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 $Λ_{p,w}$. We conclude with a characterization of the type and cotype of $Λ_{p,w}$ in the case when $Λ_{p,w}$ is a normable space.
LA - eng
KW - Lorentz spaces; quasi-Banach lattices; rearrangement invariant spaces; normability; Boyd indices; weight; weighted inequalities
UR - http://eudml.org/doc/284451
ER -