POROSITY AND THE WEIGHTED Lp-SPACES

Abstract

Let G be a locally compact group, w be a weight function on G and 1 < p, q < \infty. Recently, it has been introduced some important \sigma− c−lower porous subsets Lp(G) × Lq(G), where 1/p + 1/q < 1. Using these achievements, almost all available results connected to the existence of convolution of two functions belonging to Lp(G) are obtained. In the present work these results will be extended for the weighted case. In fact for 2< p < \infty, some important −c−lower porous subsets Lp(G,w)×Lp(G,w)are introduced.