Porosity and products of Orlicz spaces

Porosity and products of Orlicz spaces

Let be a measure space and let and be Young functions. In this paper, we, among other things, prove that the set is a - -lower porous set in , under mild restrictions on the Young functions and . This generalizes a recent result due to Gł a̧ b and Strobin (J Math Anal Appl 368:382–390, 2010 ) to mor...

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Veröffentlicht in:Positivity : an international journal devoted to the theory and applications of positivity in analysis 2013-11, Vol.17 (4), p.1009-1020
Hauptverfasser: Akbarbaglu, I., Maghsoudi, S.
Format: Artikel
Sprache:eng
Schlagworte:
Calculus of Variations and Optimal Control
Optimization
Econometrics
Fourier Analysis
Mathematical analysis
Mathematics
Mathematics and Statistics
Multiplication & division
Operator Theory
Porosity
Potential Theory
Studies
Topological manifolds
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Beschreibung
Zusammenfassung:Let be a measure space and let and be Young functions. In this paper, we, among other things, prove that the set is a - -lower porous set in , under mild restrictions on the Young functions and . This generalizes a recent result due to Gł a̧ b and Strobin (J Math Anal Appl 368:382–390, 2010 ) to more general setting of Orlicz spaces. As an application of our results, we recover a sufficient and necessary condition for Orlicz spaces to be closed under the pointwise multiplication due to Hudzik (Arch Math 44:535–538, 1985 ) and Arens et al. (J Math Anal Appl 177:386–411, 1993 ).
ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-012-0218-0