Composition operators in Orlicz-Sobolev spaces

2025/05/14 by Borowski, Michał, Cianchi, Andrea
#46E35 (47H30 46E30) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2505.09182

Abstract

The continuity of the Nemytskii operator between Orlicz-Sobolev spaces is investigated. Natural Orlicz-Sobolev versions of classical results for standard Sobolev are established. The results presented not only extend the latter, but also improve them in borderline situations. Anisotropic Orlicz-Sobolev spaces are included in our analysis. The results offered for this class of spaces are new even for customary anisotropic Sobolev spaces.

Citations

• Essentially fully anisotropic Orlicz functions and uniqueness to measure data problem
• Sharp Sobolev type embeddings on the entire Euclidean space
• The coarea formula for Sobolev mappings

Related

• Composition operators on Orlicz-Sobolev spaces
• An introduction to composition operators in Sobolev spaces
• Boundedness of composition operator in Orlicz-Morrey spaces
• Boundedness of composition operators from Lorentz spaces to Orlicz spaces
• Geometric theory of composition operators on Sobolev spaces