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arXiv 2009.024662020-09math.CVmath.FA

一类奇异区域上的Hardy空间

Hardy Spaces for a Class of Singular Domains

Anne-Katrin Gallagher, Purvi Gupta, Loredana Lanzani, Liz Vivas

备注：: 31 pages; apart from some minor changes, the terminology 'variety-deleted domain' has been changed to 'hypersurface-deleted domain'. Accepted for publication in Math. Z
DOI：: 10.1007/s00209-021-02755-1

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AI总结：

本文建立框架研究奇异区域（解析超曲面补集）继承的Hardy空间滤过结构，推广了Kerzman-Stein刚性引理，并利用恰当全纯映射将结果拓展到幂广义Hartogs三角形。

摘要：

我们建立了一个框架，用于研究在具有先验Hardy空间结构的区域中，由解析超曲面的补集所继承的Hardy空间。所继承的结构是一个滤过（filtration），我们在具体情形下研究了该滤过的多个方面。对于穿孔平面区域，我们证明了Kerzman和Stein的一个著名刚性引理的推广。在蛋形区域（egg domains）上观察到一个稳定化现象。最后，利用恰当全纯映射，我们为某些幂广义Hartogs三角形推导出Hardy空间的一个滤过，尽管这些区域超出了原始框架的适用范围。

英文摘要：

We set a framework for the study of Hardy spaces inherited by complements of analytic hypersurfaces in domains with a prior Hardy space structure. The inherited structure is a filtration, various aspects of which are studied in specific settings. For punctured planar domains, we prove a generalization of a famous rigidity lemma of Kerzman and Stein. A stabilization phenomenon is observed for egg domains. Finally, using proper holomorphic maps, we derive a filtration of Hardy spaces for certain power-generalized Hartogs triangles, although these domains fall outside the scope of the original framework.

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