Spectral multipliers for maximally subelliptic operators
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866917888392167424 |
|---|---|
| author | Zhang, Lingxiao |
| author_facet | Zhang, Lingxiao |
| contents | Consider a non-negative, self-adjoint, maximally subelliptic operator on a compact manifold. We show that the spectral multiplier is a singular integral operator under an appropriate Mihlin-Hörmander type condition. We establish the equivalence between non-isotropic Besov and Triebel-Lizorkin spaces adapted to the operator and those adapted to a Carnot-Carathéodory geometry on the manifold. We also give a Mihlin-Hörmander type condition for the boundedness of the spectral multiplier on non-isotropic $L^p$ Sobolev spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_07086 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Spectral multipliers for maximally subelliptic operators Zhang, Lingxiao Functional Analysis Analysis of PDEs Classical Analysis and ODEs 42B15, 43A85, 42B35 Consider a non-negative, self-adjoint, maximally subelliptic operator on a compact manifold. We show that the spectral multiplier is a singular integral operator under an appropriate Mihlin-Hörmander type condition. We establish the equivalence between non-isotropic Besov and Triebel-Lizorkin spaces adapted to the operator and those adapted to a Carnot-Carathéodory geometry on the manifold. We also give a Mihlin-Hörmander type condition for the boundedness of the spectral multiplier on non-isotropic $L^p$ Sobolev spaces. |
| title | Spectral multipliers for maximally subelliptic operators |
| topic | Functional Analysis Analysis of PDEs Classical Analysis and ODEs 42B15, 43A85, 42B35 |
| url | https://arxiv.org/abs/2302.07086 |