Weighted \(L^p-\)spaces on locally compact groups (Q431542)

There exists some theory of weighted \(L^p\)-algebras. If \(G\) is a locally compact group, then set \(L^p(G,\omega)=\{f: \int|f\omega|^p<\infty\}\). Usually \(p\) is assumed to be greater than or equal to 1. In this article, the author considers the case \(0<p<1\). It turns out that \(L^p(G,\omega)\) is closed under convolution if and only if \(G\) is discrete. This is also equivalent to \(L^p(G,\omega)*L^p(G,\omega)\subset L^1(G,\omega)\) and some other inclusions.