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Dichotomies for Orlicz spaces

  • Filip Strobin
Published/Copyright: May 2, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 1

Abstract

Assume that Lψ, Lψ1, …, Lψn are Orlicz spaces. We consider the size of the set Eψ(ψ1,…,ψn)={(f1,…,fn)∈Lψ1×…×Lψn: f1⋯fn∈Lψ}. We show that either it is very small (meager or σ-porous), or it is equal to Lψ1 × … × Lψn.

This work is a continuation of our previous papers, where we considered a similar problem for Lp spaces and Lorentz spaces.

Keywords: Orlicz spaces; multiplication; Baire category; porosity
MSC: Primary 46E30; 54E52; Secondary 46G99

This work has been supported by the Polish Ministry of Science and Higher Education Grant No. N N201 528 738.

  1. This paper has been communicated by Gregor Dolinar

Acknowledgement

We would like to thank the referees for a careful reading of the paper.

References

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Received: 2012-11-29
Accepted: 2013-6-28
Published Online: 2016-5-2
Published in Print: 2016-2-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0132
Keywords for this article
Orlicz spaces; multiplication; Baire category; porosity

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  5. Research Article
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