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

Ibrahim Akbarbaglu; Saeid Maghsoudi

Colloquium Mathematicae, Tome 126 (2012), p. 99-111 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $(f, g) \in L^{φ} (G) \times L^{ψ} (G) : f * g$ is well defined on G is σ-c-lower porous in $L^{φ} (G) \times L^{ψ} (G)$ . 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.

Publié le : 2012-01-01

Zbl 1267.46042

EUDML-ID : urn:eudml:doc:284235

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Ibrahim Akbarbaglu; Saeid Maghsoudi. On certain porous sets in the Orlicz space of a locally compact group. Colloquium Mathematicae, Tome 126 (2012) pp. 99-111. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm129-1-7/