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Gateaux differentiability in Orlicz–Lorentz spaces and applications

✍ Scribed by Fabian E. Levis; Hector H. Cuenya

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
190 KB
Volume
280
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let Λ~w,ϕ~ be the Orlicz–Lorentz space. We study Gateaux differentiability of the functional ψ~w,ϕ~ (f) = $ \int _{0} ^{\infty} $ ϕ (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 ψ~w,ϕ~ ‐approximants from convex closed subsets and we establish a relation between best ψ~w,ϕ~ ‐approximants and best approximants from a convex set. A characterization of best constant ψ~w,ϕ~ ‐approximants and the algorithm to construct the best constant for maximum and minimum ψ~w,ϕ~ ‐pproximants are given. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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