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arXiv · 2505.09182

Composition operators in Orlicz-Sobolev spaces

Michał Borowski·Andrea Cianchi
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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.

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Michał Borowski, Andrea Cianchi. 2025-05-14. Composition operators in Orlicz-Sobolev spaces. https://arxiv.org/abs/2505.09182

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