Composition operators of summable functions spaces

Abstract

A composition operator is a linear operator C_T on a subspace of K^X  by a point transformation T on a set X (where K denotes the scalar field) by the formula

C_T 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 K^X as L^p or W^1,p.