Hardy spaces for a class of singular domains

Gallagher, AK and Gupta, P and Lanzani, L and Vivas, L (2021) Hardy spaces for a class of singular domains. In: Mathematische Zeitschrift .

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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. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

Item Type:	Journal Article
Publication:	Mathematische Zeitschrift
Publisher:	Springer Science and Business Media Deutschland GmbH
Additional Information:	The copyright for this article belongs to Springer Science and Business Media Deutschland GmbH
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	26 Jul 2021 09:17
Last Modified:	26 Jul 2021 09:17
URI:	http://eprints.iisc.ac.in/id/eprint/68975

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