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Multiplicativity Factors for Orlicz Space Function Norms

Arens, Richard and Goldberg, Moshe and Luxemburg, W. A. J. (1993) Multiplicativity Factors for Orlicz Space Function Norms. Journal of Mathematical Analysis and Applications, 177 (2). pp. 386-411. ISSN 0022-247X. https://resolver.caltech.edu/CaltechAUTHORS:20181009-131120934

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Abstract

Let ρφ be a function norm defined by a Young function φ with respect to a measure space (T, Ω, m), and let Lφ be the Orlicz space determined by ρφ. If Lφ is an algebra, then a constant μ > 0 is called a multiplicativity factor for ρφ, if ρφ,(fg) ≤ μρφ(f) ρφ(g) for all f, g ∈ Lφ. The main objective of this paper is to give conditions under which Lφ is indeed an algebra, and to obtain in this case the best (least) multiplicativity factor for ρφ. The first of our principal results is that Lφ is an algebra if and only if or Our second main result states that if Lφ is an algebra and (T, Ω, m) is free of infinite atoms, then the best multiplicativity factor for ρφ is φ−1(1/minf if minf > 0, and x∞(φ) if minf = 0.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1006/jmaa.1993.1264DOIArticle
Additional Information:© 1993 Academic Press. Under an Elsevier user license. Received January 20, 1992.
Issue or Number:2
Record Number:CaltechAUTHORS:20181009-131120934
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20181009-131120934
Official Citation:R. Arens, M. Goldberg, W.A.J. Luxemburg, Multiplicativity Factors for Orlicz Space Function Norms, Journal of Mathematical Analysis and Applications, Volume 177, Issue 2, 1993, Pages 386-411, ISSN 0022-247X, https://doi.org/10.1006/jmaa.1993.1264. (http://www.sciencedirect.com/science/article/pii/S0022247X83712643)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:90195
Collection:CaltechAUTHORS
Deposited By: Joy Painter
Deposited On:10 Oct 2018 20:23
Last Modified:03 Oct 2019 20:22

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