Besov spaces and Schatten class Hankel operators for Hardy and Paley--Wiener spaces in higher dimensions
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909906656821248 |
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| author | Bampouras, Konstantinos Perfekt, Karl-Mikael |
| author_facet | Bampouras, Konstantinos Perfekt, Karl-Mikael |
| contents | We consider Schatten class membership of Hankel operators on Paley--Wiener spaces of convex $Ω\subset \mathbb{R}^n$, both for bounded and unbounded domains. In particular, the classical product Hardy spaces fit within our theory. For admissible domains, we develop a framework and theory of Besov spaces of Paley--Wiener type, and prove that a Hankel operator belongs to the Schatten class $S^p$ if and only if its symbol belongs to a corresponding Besov space, for $1 \leq p \leq 2$. We extend this result to all $1 \leq p < \infty$ for the classical product Hardy spaces and to $1 \leq p < 2(n+1)/(n-1)$ for the Paley--Wiener space of a bounded smooth domain $Ω\subset \mathbb{R}^n$ of strictly positive curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04184 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Besov spaces and Schatten class Hankel operators for Hardy and Paley--Wiener spaces in higher dimensions Bampouras, Konstantinos Perfekt, Karl-Mikael Functional Analysis Classical Analysis and ODEs 47B35 We consider Schatten class membership of Hankel operators on Paley--Wiener spaces of convex $Ω\subset \mathbb{R}^n$, both for bounded and unbounded domains. In particular, the classical product Hardy spaces fit within our theory. For admissible domains, we develop a framework and theory of Besov spaces of Paley--Wiener type, and prove that a Hankel operator belongs to the Schatten class $S^p$ if and only if its symbol belongs to a corresponding Besov space, for $1 \leq p \leq 2$. We extend this result to all $1 \leq p < \infty$ for the classical product Hardy spaces and to $1 \leq p < 2(n+1)/(n-1)$ for the Paley--Wiener space of a bounded smooth domain $Ω\subset \mathbb{R}^n$ of strictly positive curvature. |
| title | Besov spaces and Schatten class Hankel operators for Hardy and Paley--Wiener spaces in higher dimensions |
| topic | Functional Analysis Classical Analysis and ODEs 47B35 |
| url | https://arxiv.org/abs/2409.04184 |