The superposition operator in function spaces - A survey
type: Item
instance of: scholarly article
title: The superposition operator in function spaces - A survey
zbMATH Open document ID: 0648.47041
author: Jürgen Appell
published in: Expositiones Mathematicae
publication date: 1988-01-01T00:00:00Z
review text: 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.
reviewed by: Jürgen Appell
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 47H99
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 26A16
zbMATH DE Number: 4058267
zbMATH Keywords: boundedness
zbMATH Keywords: weak continuity
zbMATH Keywords: compactness
zbMATH Keywords: Lipschitz continuity
zbMATH Keywords: differentiability
zbMATH Keywords: asymptotic linearity
zbMATH Keywords: analyticity
zbMATH Keywords: nonlinear superposition operator
zbMATH Keywords: space S
zbMATH Keywords: Lebesgue spaces
zbMATH Keywords: Orlicz spaces
zbMATH Keywords: Lorentz spaces
zbMATH Keywords: Marcinkiewicz spaces
zbMATH Keywords: space C
zbMATH Keywords: space C k
zbMATH Keywords: Hölder spaces
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: space BV
zbMATH Keywords: space AC
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4058267