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.

中文翻译：

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一类奇异域的Hardy空间

我们为研究具有先前Hardy空间结构的域中的解析超曲面的补充所继承的Hardy空间设置了研究框架。继承的结构是一种过滤，在特定环境下将对其各个方面进行研究。对于穿孔的平面域，我们证明了Kerzman和Stein著名的刚性引理的推广。对于蛋域观察到稳定现象。最后，使用适当的全纯映射，我们为某些幂次泛化的Hartogs三角形推导了Hardy空间的过滤条件，尽管这些域不在原始框架的范围内。