Gateaux differentiability in Orlicz-Lorentz spaces and applications

F.E. LEVIS; H.H. CUENYA

MATHEMATISCHE NACHRICHTEN

Wiley-VCH

Lugar: Weinheim; Año: 2007 vol. 280 p. 1282 - 1296

0025-584X

Let Lambda_{w,phi} be the Orlicz-Lorentz space. We study Gateaux differentiability of the functional Psi_{w,phi}(f)=int_{0}^{infty} phi(f^*)w and of the Luxemburg norm. More precisely, we obtain the one-sided Gateaux derivatives in both cases and we characterize those points where the Gateaux derivative of the norm exists. We give a characterization of best Psi_{w,phi}-approximants from convex closed subsets and we establish a relation between best Psi_{w,phi}-approximants and best approximants from a convex set. A characterization of best constant Psi_{w,phi}-approximants and the algorithm to construct the best constant for maximum and minimum Psi_{w,phi}-approximants are given.