On certain porous sets in the Orlicz space of a locally compact group

Ibrahim Akbarbaglu, and Saeid Maghsoudi. "On certain porous sets in the Orlicz space of a locally compact group." Colloquium Mathematicae 129.1 (2012): 99-111. <http://eudml.org/doc/284235>.

@article{IbrahimAkbarbaglu2012,
abstract = {Let G be a locally compact group with a fixed left Haar measure. Given Young functions φ and ψ, we consider the Orlicz spaces $L^\{φ\}(G)$ and $L^\{ψ\}(G)$ on a non-unimodular group G, and, among other things, we prove that under mild conditions on φ and ψ, the set $(f,g) ∈ L^\{φ\}(G) × L^\{ψ\}(G): f*g$ is well defined on G is σ-c-lower porous in $L^\{φ\}(G) × L^\{ψ\}(G)$. 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.},
author = {Ibrahim Akbarbaglu, Saeid Maghsoudi},
journal = {Colloquium Mathematicae},
keywords = {Orlicz space; lower porous set; Young function; locally compact group; convolution},
language = {eng},
number = {1},
pages = {99-111},
title = {On certain porous sets in the Orlicz space of a locally compact group},
url = {http://eudml.org/doc/284235},
volume = {129},
year = {2012},
}

TY - JOUR
AU - Ibrahim Akbarbaglu
AU - Saeid Maghsoudi
TI - On certain porous sets in the Orlicz space of a locally compact group
JO - Colloquium Mathematicae
PY - 2012
VL - 129
IS - 1
SP - 99
EP - 111
AB - Let G be a locally compact group with a fixed left Haar measure. Given Young functions φ and ψ, we consider the Orlicz spaces $L^{φ}(G)$ and $L^{ψ}(G)$ on a non-unimodular group G, and, among other things, we prove that under mild conditions on φ and ψ, the set $(f,g) ∈ L^{φ}(G) × L^{ψ}(G): f*g$ is well defined on G is σ-c-lower porous in $L^{φ}(G) × L^{ψ}(G)$. 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.
LA - eng
KW - Orlicz space; lower porous set; Young function; locally compact group; convolution
UR - http://eudml.org/doc/284235
ER -