Circle companions of Hardy spaces of the unit disk

Raul E Curto; In Sung Hwang; Sumin Kim; Woo Young Lee

doi:10.48550/arxiv.2605.04403

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Circle companions of Hardy spaces of the unit disk

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Circle companions of Hardy spaces of the unit disk

Raul E Curto, In Sung Hwang, Sumin Kim and Woo Young Lee

ArXiv.org

Cornell University

05/06/2026

DOI: 10.48550/arxiv.2605.04403

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Preprint (Author's original) This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

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 functionhon the unit ıt disk, there exists a ``boundary function"bhon the unit ıt circle such that the mappingbh↦ his 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."

Mathematics - Complex Variables

Mathematics - Functional Analysis

Details

Title: Subtitle: Circle companions of Hardy spaces of the unit disk
Creators: Raul E Curto
In Sung Hwang
Sumin Kim
Woo Young Lee
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2605.04403
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 05/06/2026
Academic Unit: Mathematics
Record Identifier: 9985161341502771

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