# Hardy spaces for a class of singular domains

@article{Gallagher2020HardySF, 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}, year={2020} }

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…

## 3 Citations

Extendability and the $$\overline{\partial }$$ operator on the Hartogs triangle

- MathematicsMathematische Zeitschrift
- 2022

In this paper it is shown that the Hartogs triangle T in C is a uniform domain. This implies that the Hartogs triangle is a Sobolev extension domain. Furthermore, the weak and strong maximal…

Irregularity of the Bergman projection on smooth unbounded worm domains

- Mathematics
- 2022

. In this work we consider smooth unbounded worm domains Z λ in C 2 and show that the Bergman projection, densely deﬁned on the Sobolev spaces H s,p p Z λ q , p P p 1 , 8q , s ě 0, does not extend to…

von Neumann’s inequality for the Hartogs triangle

- Mathematics
- 2022

. For a commuting pair 𝑇 of bounded linear operators 𝑇 1 and 𝑇 2 on a Hilbert space ℋ , let 𝐷 𝑇 = 𝑇 ∗2 𝑇 2 − 𝑇 ∗1 𝑇 1 . If 𝑇 ∗2 𝐷 𝑇 𝑇 2 ⩽ 𝐷 𝑇 and the Taylor spectrum of 𝑇 is contained…

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