Sobolev embedding theorem and subanalytic measures
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911621891227648 |
|---|---|
| author | Valette, Guillaume |
| author_facet | Valette, Guillaume |
| contents | We focus on Borel measures that have a globally subanalytic density function. We prove, given such a measure $μ$ on a set $A$ and a globally subanalytic mapping $Φ:A\to Ω$, with $Ω$ bounded open subset of $\mathbb{R}^n$, a Sobolev embedding theorem for the Sobolev space $W^{k,p}_{Φ_*μ}(Ω)$ of the push-forward measure $Φ_*μ$. We derive an embedding of $W^{k,p}_{Φ_*μ}(Ω)$ into the space of inner Lipschitz functions and give an application to kernel theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22941 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sobolev embedding theorem and subanalytic measures Valette, Guillaume Algebraic Geometry Statistics Theory 46E35, 58C35, 32B20, 14P10 We focus on Borel measures that have a globally subanalytic density function. We prove, given such a measure $μ$ on a set $A$ and a globally subanalytic mapping $Φ:A\to Ω$, with $Ω$ bounded open subset of $\mathbb{R}^n$, a Sobolev embedding theorem for the Sobolev space $W^{k,p}_{Φ_*μ}(Ω)$ of the push-forward measure $Φ_*μ$. We derive an embedding of $W^{k,p}_{Φ_*μ}(Ω)$ into the space of inner Lipschitz functions and give an application to kernel theory. |
| title | Sobolev embedding theorem and subanalytic measures |
| topic | Algebraic Geometry Statistics Theory 46E35, 58C35, 32B20, 14P10 |
| url | https://arxiv.org/abs/2604.22941 |