Hardy Spaces for a Class of Singular Domains
| Autor: | Liz Vivas, Purvi Gupta, Anne-Katrin Gallagher, Loredana Lanzani |
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| Přispěvatelé: | Gallagher A.-K., Gupta P., Lanzani L., Vivas L. |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Class (set theory) Generalization General Mathematics Holomorphic function Structure (category theory) Rigidity (psychology) 01 natural sciences 30H10 42B30 46E22 32A25 32Q02 symbols.namesake 0103 physical sciences Filtration (mathematics) FOS: Mathematics 0101 mathematics Complex Variables (math.CV) Mathematics Lemma (mathematics) Mathematics - Complex Variables Mathematics::Complex Variables 010102 general mathematics Hardy space Hardy space point evaluatoin replroducing kernel Hilbert space Szego Functional Analysis (math.FA) Mathematics - Functional Analysis symbols 010307 mathematical physics |
| DOI: | 10.48550/arxiv.2009.02466 |
| Popis: | 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. Comment: 31 pages; apart from some minor changes, the terminology 'variety-deleted domain' has been changed to 'hypersurface-deleted domain'. Accepted for publication in Math. Z |
| Databáze: | OpenAIRE |
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