## Annals of Functional Analysis

### Uniform openness of multiplication in Orlicz spaces

#### Abstract

Let $\Phi$ and $\Psi$ be Young functions, and let $L^{\Phi}(\Omega)$ and $L^{\Psi}(\Omega)$ be corresponding Orlicz spaces on a measure space $(\Omega,\mu)$. Our aim in this paper is to prove that, under mild conditions on $\Phi$ and $\Psi$, the multiplication from $L^{\Phi}(\Omega)\times L^{\Psi}(\Omega)$ onto $L^{1}(\Omega)$ is uniformly open. This generalizes an interesting recent result due to M. Balcerzak, A. Majchrzycki, and F. Strobin in 2013.

#### Article information

Source
Ann. Funct. Anal., Volume 7, Number 4 (2016), 543-551.

Dates
Accepted: 14 March 2016
First available in Project Euclid: 31 August 2016

https://projecteuclid.org/euclid.afa/1472659940

Digital Object Identifier
doi:10.1215/20088752-3661305

Mathematical Reviews number (MathSciNet)
MR3543146

Zentralblatt MATH identifier
1354.46029

#### Citation

Akbarbaglu, Ibrahim; Maghsoudi, Saeid; Rahmani, Iraj. Uniform openness of multiplication in Orlicz spaces. Ann. Funct. Anal. 7 (2016), no. 4, 543--551. doi:10.1215/20088752-3661305. https://projecteuclid.org/euclid.afa/1472659940

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