Commutator Lipschitz Functions and Analytic Continuation
- 作者: Aleksandrov A.1
-
隶属关系:
- St.Petersburg Department of the Steklov Mathematical Institute
- 期: 卷 215, 编号 5 (2016)
- 页面: 543-551
- 栏目: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/237653
- DOI: https://doi.org/10.1007/s10958-016-2859-1
- ID: 237653
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详细
Let \( \mathfrak{F} \)0 and \( \mathfrak{F} \) be perfect subsets of the complex plane ℂ. Assume that \( \mathfrak{F} \)0 ⊂ \( \mathfrak{F} \) and the set \( \Omega \overset{\mathrm{def}}{=}\mathfrak{F}\backslash {\mathfrak{F}}_0 \) is open. We say that a continuous function f : \( \mathfrak{F} \) → ℂ is an analytic continuation of a function f0 : \( \mathfrak{F} \)0 → ℂ if f is analytic on Ω and f|\( \mathfrak{F} \)0 = f0. In the paper, it is proved that if \( \mathfrak{F} \) is bounded, then the commutator Lipschitz seminorm of the analytic continuation f coincides with the commutator Lipschitz seminorm of f0. The same is true for unbounded \( \mathfrak{F} \) if some natural restrictions concerning the behavior of f at infinity are imposed.
作者简介
A. Aleksandrov
St.Petersburg Department of the Steklov Mathematical Institute
编辑信件的主要联系方式.
Email: alex@pdmi.ras.ru
俄罗斯联邦, St.Petersburg