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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