Real Analysis Exchange

A characterization of Orlicz functions producing an additive property

Héctor Cuenya and Miguel Marano

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Abstract

It is shown that the only Luxemburg functionals that satisfy a very simply formulated property are induced by \(p\)th-power functions, \(0\lt p\lt \infty\). The known result that Orlicz spaces cannot be normed analogously to \(L_p\)-spaces follows as a consequence.

Article information

Source
Real Anal. Exchange, Volume 21, Number 2 (1995), 629-636.

Dates
First available in Project Euclid: 14 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.rae/1339694091

Mathematical Reviews number (MathSciNet)
MR1407275

Zentralblatt MATH identifier
0879.46008

Subjects
Primary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords
Orlicz function Luxemburg norm \(L_p\)-spaces

Citation

Cuenya, Héctor; Marano, Miguel. A characterization of Orlicz functions producing an additive property. Real Anal. Exchange 21 (1995), no. 2, 629--636. https://projecteuclid.org/euclid.rae/1339694091


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