Oscillation Functionals and Embeddings in Rearrangement-Invariant Spaces
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913063818493952 |
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| author | Martin, Joaquim |
| author_facet | Martin, Joaquim |
| contents | We study embeddings associated with oscillation functionals in rearrangement-invariant spaces. More precisely, given a positive function \(ψ\), we analyze how the interaction between the geometry of the underlying space and the growth of \(ψ\) determines the behaviour of these embeddings, leading to a natural classification into subcritical, supercritical and critical regimes.
We prove that in the critical regime logarithmic refinements of Hansson type appear, governed by a deviation function associated with the quotient \(ψ/φ_X\), where \(φ_X\) is the fundamental function of the underlying space. This leads to explicit Hansson-type targets and, in the bounded case of the deviation function, to Trudinger-type consequences. The results recover and extend several classical endpoint embeddings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05804 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Oscillation Functionals and Embeddings in Rearrangement-Invariant Spaces Martin, Joaquim Functional Analysis 46E30, 46E35, 46B70 We study embeddings associated with oscillation functionals in rearrangement-invariant spaces. More precisely, given a positive function \(ψ\), we analyze how the interaction between the geometry of the underlying space and the growth of \(ψ\) determines the behaviour of these embeddings, leading to a natural classification into subcritical, supercritical and critical regimes. We prove that in the critical regime logarithmic refinements of Hansson type appear, governed by a deviation function associated with the quotient \(ψ/φ_X\), where \(φ_X\) is the fundamental function of the underlying space. This leads to explicit Hansson-type targets and, in the bounded case of the deviation function, to Trudinger-type consequences. The results recover and extend several classical endpoint embeddings. |
| title | Oscillation Functionals and Embeddings in Rearrangement-Invariant Spaces |
| topic | Functional Analysis 46E30, 46E35, 46B70 |
| url | https://arxiv.org/abs/2604.05804 |