Porosity and products of Orlicz spaces

Porosity and products of Orlicz spaces Let $$(\Omega , \Sigma , \mu )$$ be a measure space and let $$\varphi _1, \ldots , \varphi _n$$ and $$\varphi $$ be Young functions. In this paper, we, among other things, prove that the set $$E=\{(f_1, \ldots ,f_n)\in M^{\varphi _1}\times \cdots \times M^{\varphi _n}:\, N_\varphi (f_1\cdots f_n)<\infty \}$$ is a $$\sigma $$ - $$c$$ -lower porous set in $$M^{\varphi _1}\times \cdots \times M^{\varphi _n}$$ , under mild restrictions on the Young functions $$\varphi _1, \ldots , \varphi _n$$ and $$\varphi $$ . 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). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

Porosity and products of Orlicz spaces

Loading next page...
 
/lp/springer_journal/porosity-and-products-of-orlicz-spaces-6MYwdzKsIT
Publisher
Springer Basel
Copyright
Copyright © 2012 by Springer Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-012-0218-0
Publisher site
See Article on Publisher Site

Abstract

Let $$(\Omega , \Sigma , \mu )$$ be a measure space and let $$\varphi _1, \ldots , \varphi _n$$ and $$\varphi $$ be Young functions. In this paper, we, among other things, prove that the set $$E=\{(f_1, \ldots ,f_n)\in M^{\varphi _1}\times \cdots \times M^{\varphi _n}:\, N_\varphi (f_1\cdots f_n)<\infty \}$$ is a $$\sigma $$ - $$c$$ -lower porous set in $$M^{\varphi _1}\times \cdots \times M^{\varphi _n}$$ , under mild restrictions on the Young functions $$\varphi _1, \ldots , \varphi _n$$ and $$\varphi $$ . 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).

Journal

PositivitySpringer Journals

Published: Dec 16, 2012

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off