On certain porous sets in the Orlicz space of a locally compact group
Volume 129 / 2012
Colloquium Mathematicum 129 (2012), 99-111
MSC: Primary 46E30, 43A15; Secondary 54E52.
DOI: 10.4064/cm129-1-7
Abstract
Let $G$ be a locally compact group with a fixed left Haar measure. Given Young functions $\varphi $ and $\psi $, we consider the Orlicz spaces $L^\varphi (G)$ and $L^\psi (G)$ on a non-unimodular group $G$, and, among other things, we prove that under mild conditions on $\varphi $ and $\psi $, the set $\{(f,g)\in L^\varphi (G)\times L^\psi (G): f\ast g$ is well defined on $G\} $ is $\sigma $-$c$-lower porous in $L^\varphi (G)\times L^\psi (G)$. This answers a question raised by Głąb and Strobin in 2010 in a more general setting of Orlicz spaces. We also prove a similar result for non-compact locally compact groups.
