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

• Autorzy: Ibrahim Akbarbaglu , Saeid Maghsoudi
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 43A15: L p -spaces and other function spaces on groups, semigroups, etc.
• 54E52: Baire category, Baire spaces
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2012
• Tom: 129
• Numer: 1
• Strony: 99-111

Daty

wydano

2012

Twórcy

autor

Ibrahim Akbarbaglu

• Department of Mathematics, University of Zanjan, Zanjan 45195-313, Iran

autor

Saeid Maghsoudi

• Department of Mathematics, University of Zanjan, Zanjan 45195-313, Iran

Identyfikatory

DOI

10.4064/cm129-1-7