The superposition operator in function spaces - A survey
The survey gives a systematic account of the basic analytical and topological properties (boundedness, continuity, weak continuity, compactness, Lipschitz continuity, differentiability, asymptotic linearity, analyticity) of the nonlinear superposition operator \(Fu(x)=f(x,u(x))\) in various function spaces (the space S, Lebesgue spaces, Orlicz spaces, Lorentz spaces, Marcinkiewicz spaces, the space C, the space C k, Hölder spaces, Sobolev spaces, the space BV, the space AC). The bibliography contains about 300 items covering the period from 1918 to 1988.
scientific article; zbMATH DE number 4058267