TYPE AND ORDER CONVEXITY OF MARCINKIEWICZ AND LORENTZ SPACES AND APPLICATIONS
Glasgow mathematical journal, Tome 47 (2005) no. 1, pp. 123-137
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We consider order and type properties of Marcinkiewicz and Lorentz function spaces. We show that if $0, a $p$-normable quasi-Banach space is natural (i.e. embeds into a $q$-convex quasi-Banach lattice for some $q>0$) if and only if it is finitely representable in the space $L_{p,\infty}.$ We also show in particular that the weak Lorentz space $L_{1,\infty}$ do not have type $1$, while a non-normable Lorentz space $L_{1,p}$ has type $1$. We present also criteria for upper $r$-estimate and $r$-convexity of Marcinkiewicz spaces.
KALTON, NIGEL J.; KAMIŃSKA, ANNA. TYPE AND ORDER CONVEXITY OF MARCINKIEWICZ AND LORENTZ SPACES AND APPLICATIONS. Glasgow mathematical journal, Tome 47 (2005) no. 1, pp. 123-137. doi: 10.1017/S0017089504002204
@article{10_1017_S0017089504002204,
author = {KALTON, NIGEL J. and KAMI\'NSKA, ANNA},
title = {TYPE {AND} {ORDER} {CONVEXITY} {OF} {MARCINKIEWICZ} {AND} {LORENTZ} {SPACES} {AND} {APPLICATIONS}},
journal = {Glasgow mathematical journal},
pages = {123--137},
year = {2005},
volume = {47},
number = {1},
doi = {10.1017/S0017089504002204},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089504002204/}
}
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