Convolution on weighted Lp -spaces of locally compact groups

Abstract

Let G be a locally compact group and 2 < p < ∞. We have recently considered the property that convolutions of functions in the L p -space of G exist, and have shown that this is equivalent to compactness of G. Here, we study this property on the weighted Lp -space of G; as the main result, we prove that G is σ -compact if convolutions of functions in the weighted Lp -space of G exist. Copyright © Academia Românǎ 2006.