On products of Sobolev-Orlicz spaces

DOI10.1017/S0004972700028598zbMath0707.46023MaRDI QIDQ3488711

Grahame Hardy, Jürgen Appell

Publication date: 1990

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Orlicz-Sobolev spacesuperposition operatornonlinear Nemytskii operatoroperation of multiplication by a fixed function

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)

Cites Work

• Unnamed Item
• On products of Orlicz spaces
• Every superposition operator mapping one Sobolev space into another is continuous
• Interpolation of operators of weak type
• A characterization of first order nonlinear partial differential operators on Sobolev spaces
• Continuity of certain Nemitsky operators on Sobolov spaces and the chain rule
• Orlicz-Sobolev spaces and imbedding theorems
• Absolute continuity on tracks and mappings of Sobolev spaces
• Nemitsky operators on Sobolev spaces
• Complete Characterization of Functions Which Act, Via Superposition, on Sobolev Spaces
• ON THE DEGENERATION OF THE CLASS OF DIFFERENTIABLE SUPERPOSITION OPERATORS IN FUNCTION SPACES
• Representation Theorems for Nonlinear Disjointly Additive Functionals and Operators on Sobolev Spaces
• Superposition mappings which operate on Sobolev spaces
• Nonlinear Elliptic Boundary Value Problems for Equations With Rapidly (Or Slowly) Increasing Coefficients
• [Russian Text Ignored.]

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