Translation invariant linear functionals in Orlicz spaces on locally compact groups

Ya. A. Kopylov

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: We study the existence of nontrivial translation invariant functionals on Orlicz spaces $L^\Phi(G)$ and Morse–Transue spaces $M^\Phi(G)$, where $G$ is a locally compact group and $\Phi$ is an $N$-function.

Keywords: locally compact group, Orlicz space, translation invariant linear functional.

UDC: 517.986.6:512.546.3

MSC: MSC 43A07, 43A15

Received: 11.03.2025
Revised: 12.04.2025
Accepted: 11.06.2025

DOI: 10.33048/smzh.2025.66.510

 English version: Siberian Mathematical Journal, 2025, 66:5, 1212–1217