ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. LXXIII, 1 (2004)
p. 31 – 41
Gateaux Differentiability for Functionals of Type Orlicz-Lorentz
H. H. Cuenya and F. E. Levis
Abstract.
Let $(\Omega,{\mathcal A},\mu)$ be a $\sigma$-finite nonatomic
measure space and let $\Lambda_{w,\phi}$ be the Orlicz-Lorentz
space. We study the Gateaux differentiability of the functional
$\Psi_{w,\phi}(f)= \smallint\limits_{0}^{\infty} \phi(f^*)w$. More
precisely we give an exact characterization of those points in the
Orlicz-Lorentz space $\Lambda_{w,\phi}$ where the Gateaux
derivative exists. This paper extends known results already on
Lorent spaces, $L_{w,q}$, $1<q<\infty$. The case $q=1$, it has
been considered.
AMS subject classification:
46E30; Secondary: 46B20.
Keywords:
Gateaux derivative, Orlicz-Lorentz space.
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