Circle companions of Hardy spaces of the unit disk
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918490474020864 |
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| author | Curto, Raul E. Hwang, In Sung Kim, Sumin Lee, Woo Young |
| author_facet | Curto, Raul E. Hwang, In Sung Kim, Sumin Lee, Woo Young |
| contents | This paper gives a complete answer to the following problem: Find the circle companion of the Hardy space of the unit disk with values in the space of all bounded linear operators between two separable Hilbert spaces. Classically, the problem asks whether for each function $h$ on the unit {\it disk}, there exists a ``boundary function" $bh$ on the unit {\it circle} such that the mapping $bh\mapsto h$ is an isometric isomorphism between Hardy spaces of the unit circle and the unit disk with values in some Banach space. For the case of bounded linear operator-valued functions, we construct a Hardy space of the unit circle such that its elements are SOT measurable, and their norms are integrable: indeed, this new space is isometrically isomorphic to the Hardy space of the unit disk via a ``strong Poisson integral." |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04403 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Circle companions of Hardy spaces of the unit disk Curto, Raul E. Hwang, In Sung Kim, Sumin Lee, Woo Young Complex Variables Functional Analysis 42B30, 30H10, 46E40, 46E30 (Primary) This paper gives a complete answer to the following problem: Find the circle companion of the Hardy space of the unit disk with values in the space of all bounded linear operators between two separable Hilbert spaces. Classically, the problem asks whether for each function $h$ on the unit {\it disk}, there exists a ``boundary function" $bh$ on the unit {\it circle} such that the mapping $bh\mapsto h$ is an isometric isomorphism between Hardy spaces of the unit circle and the unit disk with values in some Banach space. For the case of bounded linear operator-valued functions, we construct a Hardy space of the unit circle such that its elements are SOT measurable, and their norms are integrable: indeed, this new space is isometrically isomorphic to the Hardy space of the unit disk via a ``strong Poisson integral." |
| title | Circle companions of Hardy spaces of the unit disk |
| topic | Complex Variables Functional Analysis 42B30, 30H10, 46E40, 46E30 (Primary) |
| url | https://arxiv.org/abs/2605.04403 |