Composition operators of summable functions spaces

Abstract

A composition operator is a linear operator CT on a subspace of KX  by a point transformation T on a set X (where K denotes the scalar field) by the formula CT f(x) :=f ∘ T(x). We give some necessary and/or sufficient conditions under which the map T induces a continuous composition operator on suitable topological subspaces of summable functions of KX as Lp or W1,p.