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.
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