Geodesic
Gateaux Differentiability for Functionals of Type Orlicz-Lorentz
Acta mathematica Universitatis Comenianae, Tome 73 (2004) no. 1 
H. H. Cuenya; F. E. Levis. Gateaux Differentiability for Functionals of Type Orlicz-Lorentz. Acta mathematica Universitatis Comenianae, Tome 73 (2004) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2004_73_1_a2/
@article{AMUC_2004_73_1_a2,
     author = {H. H. Cuenya and F. E. Levis},
     title = {Gateaux {Differentiability} for {Functionals} of {Type} {Orlicz-Lorentz}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2004},
     volume = {73},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2004_73_1_a2/}
}
TY  - JOUR
AU  - H. H. Cuenya
AU  - F. E. Levis
TI  - Gateaux Differentiability for Functionals of Type Orlicz-Lorentz
JO  - Acta mathematica Universitatis Comenianae
PY  - 2004
VL  - 73
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/AMUC_2004_73_1_a2/
ID  - AMUC_2004_73_1_a2
ER  - 
%0 Journal Article
%A H. H. Cuenya
%A F. E. Levis
%T Gateaux Differentiability for Functionals of Type Orlicz-Lorentz
%J Acta mathematica Universitatis Comenianae
%D 2004
%V 73
%N 1
%U http://geodesic.mathdoc.fr/item/AMUC_2004_73_1_a2/
%F AMUC_2004_73_1_a2

Voir la notice de l'article provenant de la source Comenius University

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. The case $q=1$, it has been considered.