De Cicco, Virginia; Marino, Giuseppe Composition operators on summable functions spaces. (English) Zbl 0724.47015 Matematiche 44, No. 1, 3-19 (1989). Summary: A composition operator is a linear operator \(C_ T\) on a subspace of \({\mathbb{K}}^ X\) by a point transformation T on a set X (where \({\mathbb{K}}\) denotes the scalar field) by the formula \(C_ Tf(x):=f\circ T(x).\) 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 \({\mathbb{K}}^ X\) as \(L^ p\) or \(W^{1,p}\). Cited in 1 Document MSC: 47B38 Linear operators on function spaces (general) 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems Keywords:composition operator; continuous composition operator PDFBibTeX XMLCite \textit{V. De Cicco} and \textit{G. Marino}, Matematiche 44, No. 1, 3--19 (1989; Zbl 0724.47015)