Fractional Sobolev spaces related to an ultraparabolic operator
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917889123024896 |
|---|---|
| author | Pesce, Antonello Portaro, Sascha |
| author_facet | Pesce, Antonello Portaro, Sascha |
| contents | We propose a functional framework of fractional Sobolev spaces for a class of ultra-parabolic Kolmogorov type operators satisfying the weak Hörmander condition. We characterize these spaces as real interpolation of natural order intrinic Sobolev spaces recently introduced in [27], and prove continuous embeddings into $L^p$ and intrinsic Hölder spaces from [24]. These embeddings naturally extend the standard Euclidean ones, coherently with the homogeneous structure of the associated Kolmogorov group. Our approach to interpolation is based on approximation of intrinsically regular functions, the latter heavily relying on integral estimates of the intrinsic Taylor remainder. The embeddings exploit the aforementioned interpolation property and the corresponding embeddings of natural order intrinsic spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_05898 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional Sobolev spaces related to an ultraparabolic operator Pesce, Antonello Portaro, Sascha Analysis of PDEs Functional Analysis We propose a functional framework of fractional Sobolev spaces for a class of ultra-parabolic Kolmogorov type operators satisfying the weak Hörmander condition. We characterize these spaces as real interpolation of natural order intrinic Sobolev spaces recently introduced in [27], and prove continuous embeddings into $L^p$ and intrinsic Hölder spaces from [24]. These embeddings naturally extend the standard Euclidean ones, coherently with the homogeneous structure of the associated Kolmogorov group. Our approach to interpolation is based on approximation of intrinsically regular functions, the latter heavily relying on integral estimates of the intrinsic Taylor remainder. The embeddings exploit the aforementioned interpolation property and the corresponding embeddings of natural order intrinsic spaces. |
| title | Fractional Sobolev spaces related to an ultraparabolic operator |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2501.05898 |