$\Phi$-Harmonic Functions on Discrete Groups and First ${\ell }^{\Phi }$-Cohomology

Yaroslav Kopylov, Roman Panenko

We study the first cohomology groups of a countable discrete group $G$ with coefficients in a $G$-module ${\ell }^{\Phi }(G)$, where $\Phi$ is an $N$-function of class ${\Delta }_2(0)\cap {\nabla }_2(0)$…