Boundedness and compactness kernel theorem for $α$-modulation spaces
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913522139529216 |
|---|---|
| author | Zhao, Guoping Guo, Weichao |
| author_facet | Zhao, Guoping Guo, Weichao |
| contents | This paper is devoted to establishing the kernel theorems for $α$-modulation spaces in terms of boundedness and compactness. We characterize the boundedness of a linear operator $A$ from an $α$-modulation space $M^p_α(\mathbb{R}^d)$ into another $α$-modulation space $M^q_α(\mathbb{R}^d)$, by the membership of its distributional kernel in mixed $α$-modulation spaces. We also characterize the compactness of $A$ by means of the kernel in a certain closed subspace of mixed $α$-modulation spaces. The proofs are based on the viewpoint that the action of the linear operator on certain function space can be reduced to the action on the suitable atoms of this function space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19193 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Boundedness and compactness kernel theorem for $α$-modulation spaces Zhao, Guoping Guo, Weichao Functional Analysis Classical Analysis and ODEs This paper is devoted to establishing the kernel theorems for $α$-modulation spaces in terms of boundedness and compactness. We characterize the boundedness of a linear operator $A$ from an $α$-modulation space $M^p_α(\mathbb{R}^d)$ into another $α$-modulation space $M^q_α(\mathbb{R}^d)$, by the membership of its distributional kernel in mixed $α$-modulation spaces. We also characterize the compactness of $A$ by means of the kernel in a certain closed subspace of mixed $α$-modulation spaces. The proofs are based on the viewpoint that the action of the linear operator on certain function space can be reduced to the action on the suitable atoms of this function space. |
| title | Boundedness and compactness kernel theorem for $α$-modulation spaces |
| topic | Functional Analysis Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2409.19193 |