Superposition in homogeneous and vector valued Sobolev spaces

DOI10.1090/S0002-9947-2010-05150-5zbMath1211.46028OpenAlexW1985698122MaRDI QIDQ3056582

Gérard Bourdaud

Publication date: 12 November 2010

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-2010-05150-5

zbMATH Keywords

superposition operatorshomogeneous Sobolev spacevector-valued Sobolev space

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30)

Related Items (11)

Composition operators on Herz-type Triebel-Lizorkin spaces with application to semilinear parabolic equations ⋮ On the composition operators on Besov and Triebel–Lizorkin spaces with power weights ⋮ Composition in critical Besov spaces ⋮ AN INTRODUCTION TO COMPOSITION OPERATORS IN SOBOLEV SPACES ⋮ Dahlberg degeneracy for homogeneous Besov and Triebel–Lizorkin spaces ⋮ Nemytzkij operators on Sobolev spaces with power weights. I ⋮ Composition operators acting on Besov spaces on the real line ⋮ Projection-Based Finite Elements for Nonlinear Function Spaces ⋮ Realization of homogeneous Triebel - Lizorkin spaces with $p=\infty $ and characterizations via differences ⋮ Composition operators on Lizorkin-Triebel spaces ⋮ Continuity of composition operators in Sobolev spaces

Cites Work

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• Remarks on the symbolic calculus in vector valued Besov spaces
• Réalisations des espaces de Besov homogènes. (Realization of homogeneous Besov spaces)
• On the existence of capacitary strong type estimates in \(R^n\)
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• An elementary proof of the Brezis and Mironescu theorem on the composition operator in fractional Sobolev spaces
• Sur les fonctions qui operent sur l'espace \(\hat A^ 2\)
• Towards sharp superposition theorems in Besov and Lizorkin-Triebel spaces
• Complete Characterization of Functions Which Act, Via Superposition, on Sobolev Spaces
• Composition Operators on Potential Spaces
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