Porosity and the L p-conjecture

Abstract

Abstract.Recently, Abtahi, Nasr-Isfahani, and Rejali [1] have shown that if G is a locally compact but not compact topological group and p > 2, then there are two functions, f and g, such that the convolution f g is equal to ∞ on some set of positive measure. In the paper we show the nonexistence of f g on a set of positive measure for (f, g) from a complement of a σ-porous set. Mathematics Subject Classification (2000). Primary 43A15, 46E30; Secondary 46G99, 54E52.