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arXiv · 2512.13160

Inhomogeneous Sobolev and Besov Spaces: Embeddings and prevalent smoothness

Quentin Rible
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Abstract

In this article, we introduce inhomogeneous Sobolev spaces that naturally generalise the standard Sobolev-Slobodeckij spaces. The inhomogeneity of these spaces is governed by a set function $\mu$, referred to as an environment. In the case where $\mu$ is an almost doubling set function, we relate these new spaces with inhomogeneous Besov spaces recently introduced by Barral-Seuret in 2023. When $\mu$ is in addition a capacity, wee also prove that prevalent elements in such spaces are multifractal (with a singularity spectrum that we determine), completing previous Baire generic results already obtained.

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Quentin Rible. 2025-12-15. Inhomogeneous Sobolev and Besov Spaces: Embeddings and prevalent smoothness. https://arxiv.org/abs/2512.13160

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