Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 11, Number 3 (2017), 636-660.
Normed Orlicz function spaces which can be quasi-renormed with easily calculable quasinorms
We are interested in the widest possible class of Orlicz functions such that the easily calculable quasinorm if and if , on the Orlicz space generated by , is equivalent to the Luxemburg norm . To do this, we use a suitable -condition, lower and upper Simonenko indices and for the generating function , numbers satisfying , and an embedding of into a suitable Köthe function space . We take as the Lebesgue spaces with , when the measure is nonatomic and finite, and the weighted Lebesgue spaces , with and a suitable weight function , when the measure is nonatomic infinite but -finite. We also use condition if and condition if , proving their necessity in most of the considered cases. Our results seem important for applications of Orlicz function spaces.
Banach J. Math. Anal., Volume 11, Number 3 (2017), 636-660.
Received: 7 June 2016
Accepted: 29 September 2016
First available in Project Euclid: 9 June 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Secondary: 46B03: Isomorphic theory (including renorming) of Banach spaces 46B42: Banach lattices [See also 46A40, 46B40]
Foralewski, Paweł; Hudzik, Henryk; Kaczmarek, Radosław; Krbec, Miroslav. Normed Orlicz function spaces which can be quasi-renormed with easily calculable quasinorms. Banach J. Math. Anal. 11 (2017), no. 3, 636--660. doi:10.1215/17358787-2017-0009. https://projecteuclid.org/euclid.bjma/1496973700