Generalized weighted algebras (Q997589)

Let \(G\) be an abelian locally compact group. The authors study the spaces \(L^p_{\omega}(G,E)\), \(1<p<\infty\). Roughly speaking, they consist of functions from \(G\) to a locally convex topological algebra \(E\), such that \(p\)-th powers of their \(E\)-seminorms are Haar summable with a weight \(\omega\). Under certain conditions, these spaces are locally convex algebras with respect to the convolution multiplication. The authors provide some information about the structure of such algebras.