Potential theory and boundary behavior in the Drury-Arveson space
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913540136239104 |
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| author | Chalmoukis, Nikolaos Hartz, Michael |
| author_facet | Chalmoukis, Nikolaos Hartz, Michael |
| contents | We develop a notion of capacity for the Drury-Arveson space $H^2_d$ of holomorphic functions on the Euclidean unit ball. We show that every function in $H^2_d$ has a non-tangential limit (in fact Korányi limit) at every point in the sphere outside of a set of capacity zero. Moreover, we prove that the capacity zero condition is sharp, and that it is equivalent to being totally null for $H^2_d$. We also provide applications to cyclicity. Finally, we discuss generalizations of these results to other function spaces on the ball. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07773 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Potential theory and boundary behavior in the Drury-Arveson space Chalmoukis, Nikolaos Hartz, Michael Functional Analysis Complex Variables Primary 46E22, Secondary 31B15, 32U20 We develop a notion of capacity for the Drury-Arveson space $H^2_d$ of holomorphic functions on the Euclidean unit ball. We show that every function in $H^2_d$ has a non-tangential limit (in fact Korányi limit) at every point in the sphere outside of a set of capacity zero. Moreover, we prove that the capacity zero condition is sharp, and that it is equivalent to being totally null for $H^2_d$. We also provide applications to cyclicity. Finally, we discuss generalizations of these results to other function spaces on the ball. |
| title | Potential theory and boundary behavior in the Drury-Arveson space |
| topic | Functional Analysis Complex Variables Primary 46E22, Secondary 31B15, 32U20 |
| url | https://arxiv.org/abs/2410.07773 |