$$\phi (L)$$-Factorable Operators on $$L^{P}(G)$$ for a Locally Compact Abelian Group

Abstract

Let G be a locally compact abelian group, $$\phi $$ be a topological isomorphism on G, and L be a uniform lattice in G. We provide a development of the $$L^{ 1} (G/\phi (L)) $$ function-valued product on $$ L^{ p} (G)$$ called $$(\phi (L),p)$$ -bracket product, where $$ 1<p<\infty $$ . Among other things, we study $$\phi (L)$$ -factorable operators and we prove Riesz representation type theorem for $$ L^{ p} (G)$$ .