Convolution on Lp-spaces of a locally compact group

Abstract

We have recently shown that, for 2 < p < ∞, a locally compact group G is compact if and only if the convolution multiplication f * g exists for all f, g ∈ Lp(G). Here, we study the existence of f * g for all f, g ∈ Lp(G) in the case where 0 < p ≤ 2. Also, for 0 < p < ∞, we offer some necessary and sufficient conditions for Lp(G) * Lp(G) to be contained in certain function spaces on G. © 2013 Versita Warsaw and Springer-Verlag Wien.