Hardy spaces for a class of singular domains

  title={Hardy spaces for a class of singular domains},
  author={Anne-Katrin Gallagher and Purvi Gupta and Loredana Lanzani and Liz Raquel Vivas},
  journal={arXiv: Complex Variables},
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… 
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