Gateaux Differentiability for Functionals of Type Orlicz-Lorentz

F.E. LEVIS; H. H. CUENYA

ACTA MATHEMATICA UNIVERSATIS COMENIANAE

Comenius University

Lugar: Bratislava; Año: 2004 vol. 73 p. 31 - 41

0862-9544

Let $(Omega,Cal A,mu)$ 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$Psi_{w,phi}(f)= smallintlimits_{0}^{infty} phi(f^*)w.$ 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