Continuity of the superposition operator on Orlicz-Sobolev spaces

DOI10.1017/S0004972700009576zbMath0810.47060MaRDI QIDQ4312393

Grahame Hardy, H. B. Thompson

Publication date: 30 November 1994

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

zbMATH Keywords

automatic continuityBorel measurable functionSobolev-Orlicz spacesautonomous Nemytskij operator

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 (1)

Localization method for the solutions of nonhomogeneous operator equations

Cites Work

• Every superposition operator mapping one Sobolev space into another is continuous
• Strongly extreme points in Köthe-Bochner spaces
• Orlicz-Sobolev spaces and imbedding theorems
• Absolute continuity on tracks and mappings of Sobolev spaces
• Nonlinear Elliptic Boundary Value Problems for Equations With Rapidly (Or Slowly) Increasing Coefficients

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