Universal multipliers for Sub-Hardy Hilbert spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909353402957824 |
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| author | Malman, Bartosz Seco, Daniel |
| author_facet | Malman, Bartosz Seco, Daniel |
| contents | To every non-extreme point $b$ of the unit ball of $\hil^\infty$ of the unit disk there corresponds a Pythagorean mate, a bounded outer function $a$ satisfying the equation $|a|^2 + |b|^2 = 1$ on the boundary of the disk. We study universal, i.e., simultaneous multipliers for families of de Branges-Rovnyak spaces $\hb$, and develop a general framework for this purpose. Our main results include a new proof of the Davis-McCarthy universal multiplier theorem for the class of all non-extreme spaces $\hb$, a characterization of the Lipschitz classes as the universal multipliers for spaces $\hb$ for which the quotient $b/a$ is contained in a Hardy space, and a similar characterization of the Gevrey classes as the universal multipliers for spaces $\hb$ for which $b/a$ is contained in a Privalov class. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_13438 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal multipliers for Sub-Hardy Hilbert spaces Malman, Bartosz Seco, Daniel Functional Analysis Complex Variables Primary 30H45, Secondary 47B32 To every non-extreme point $b$ of the unit ball of $\hil^\infty$ of the unit disk there corresponds a Pythagorean mate, a bounded outer function $a$ satisfying the equation $|a|^2 + |b|^2 = 1$ on the boundary of the disk. We study universal, i.e., simultaneous multipliers for families of de Branges-Rovnyak spaces $\hb$, and develop a general framework for this purpose. Our main results include a new proof of the Davis-McCarthy universal multiplier theorem for the class of all non-extreme spaces $\hb$, a characterization of the Lipschitz classes as the universal multipliers for spaces $\hb$ for which the quotient $b/a$ is contained in a Hardy space, and a similar characterization of the Gevrey classes as the universal multipliers for spaces $\hb$ for which $b/a$ is contained in a Privalov class. |
| title | Universal multipliers for Sub-Hardy Hilbert spaces |
| topic | Functional Analysis Complex Variables Primary 30H45, Secondary 47B32 |
| url | https://arxiv.org/abs/2410.13438 |