Hilbertian Hardy--Sobolev Spaces on Tube Domains over Convex Cones
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912972343869440 |
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| author | Li, Haichou Qian, Tao |
| author_facet | Li, Haichou Qian, Tao |
| contents | We introduce Hilbertian Hardy--Sobolev spaces on tube domains over convex cones and develop their structural theory from a Fourier-analytic point of view. We first establish a Paley--Wiener type representation, which identifies these spaces with weighted $L^2$ spaces on the dual cone and reveals their intrinsic Fourier structure. This representation leads naturally to a Hardy--Sobolev decomposition theorem for boundary Sobolev spaces on $\mathbb{R}^d$. Building on these structural results, we derive explicit reproducing kernels and characterize Carleson measures for the Hilbertian Hardy--Sobolev spaces. As a preliminary operator-theoretic application, we also derive basic consequences for multipliers and weighted composition operators on these spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17285 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hilbertian Hardy--Sobolev Spaces on Tube Domains over Convex Cones Li, Haichou Qian, Tao Functional Analysis We introduce Hilbertian Hardy--Sobolev spaces on tube domains over convex cones and develop their structural theory from a Fourier-analytic point of view. We first establish a Paley--Wiener type representation, which identifies these spaces with weighted $L^2$ spaces on the dual cone and reveals their intrinsic Fourier structure. This representation leads naturally to a Hardy--Sobolev decomposition theorem for boundary Sobolev spaces on $\mathbb{R}^d$. Building on these structural results, we derive explicit reproducing kernels and characterize Carleson measures for the Hilbertian Hardy--Sobolev spaces. As a preliminary operator-theoretic application, we also derive basic consequences for multipliers and weighted composition operators on these spaces. |
| title | Hilbertian Hardy--Sobolev Spaces on Tube Domains over Convex Cones |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2603.17285 |