论文标题
一类奇异领域的耐寒空间
Hardy Spaces for a Class of Singular Domains
论文作者
论文摘要
我们设定了一个框架，以研究通过具有先前耐硬的空间结构的域中的分析性超曲面的补充。继承的结构是一种过滤，在特定设置中研究了其各个方面。对于刺穿的平面域，我们证明了Kerzman和Stein著名的刚性引理的概括。对于卵域观察到稳定现象。最后，使用适当的全态图，我们得出了某些功率将来的Hartogs三角形的耐力空间过滤，尽管这些域落在原始框架的范围之内。
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.
