Hardy spaces for a class of singular domains

A. K. Gallagher, P. Gupta, L. Lanzani, L. Vivas

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
JournalMathematische Zeitschrift
DOIs
StateAccepted/In press - 2021

ASJC Scopus subject areas

  • Mathematics(all)

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