Remarks on the superposition operator problem in various function spaces

DOI10.1080/17476930903568332zbMath1216.47089OpenAlexW2006944435MaRDI QIDQ4931829

Peter P. Zabreĭko, Jürgen Appell

Publication date: 1 October 2010

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476930903568332

zbMATH Keywords

function spacesnonlinear superposition operators

Mathematics Subject Classification ID

Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15)

Related Items (8)

Functional calculus on BMO-type spaces of Bourgain, Brezis and Mironescu ⋮ Counterexamples on compositions ⋮ Superposition operators between weighted Banach spaces of analytic functions of controlled growth ⋮ A survey on composition operators on some function spaces ⋮ On generalized common quasi-eigenvector problems ⋮ Functions with antiderivative. II: Products and compositions ⋮ Some counterexamples for your calculus course ⋮ Continuity, monotonicity, oscillation, variation: obvious and surprising aspects

Cites Work

• Le calcul fonctionnel dans les espaces de Sobolev. (Functional calculus in Sobolev spaces)
• Fonctions qui opèrent sur les espaces de Sobolev. (Functions that operate on Sobolev spaces)
• Functional calculus in fractional Sobolev spaces
• Functional calculus in certainLizorkin-Triebel spaces
• Functional calculus on \(BMO\) and related spaces
• A composition property in the space \(H^s\)
• Functions which operate on Besov spaces
• Towards sharp superposition theorems in Besov and Lizorkin-Triebel spaces
• Superposition operators and functions of bounded \(p\)-variation. II
• On operators in generalized Hölder spaces
• Functional Calculus in Hölder-Zygmund Spaces
• Theoremes de Bornage Pour L'Operateur de Nemyckii Dans Les Espaces Ideaux
• Superposition mappings which operate on Sobolev spaces
• Unnamed Item

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