Abstract
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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L. Lanzani and L. Vivas were supported in part by the National Science Foundation (DMS-1901978 and DMS-1800777). P. Gupta was supported in part by a UGC CAS-II grant (Grant No. F.510/25/CAS-II/ 2018(SAP-I)). Part of this work took place at the Banff International Research station during a workshop of the Women in Analysis (WoAn), an AWM Research Network. We are grateful to the Institute for its kind hospitality and to the Association of Women in Mathematics for its generous support. We also wish to thank Mei-Chi Shaw for providing the inspiration for this work, Björn Gustafsson for offering helpful feedback on an earlier version of this manuscript, and the anonymous referee for their useful comments.
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Gallagher, AK., Gupta, P., Lanzani, L. et al. Hardy spaces for a class of singular domains. Math. Z. 299, 2171–2197 (2021). https://doi.org/10.1007/s00209-021-02755-1
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DOI: https://doi.org/10.1007/s00209-021-02755-1