# 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}
}
• Published 5 September 2020
• Mathematics
• arXiv: Complex Variables
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…
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## References

SHOWING 1-10 OF 46 REFERENCES
On Hardy spaces in complex ellipsoids
A fundamental tool in the study of holomorphic functions of one complex variable is the Cauchy integral formula. Hence when studying holomorphic functions in a domain fl. C C one wants a suitable
Hardy and Bergman spaces on hyperconvex domains and their composition operators
• Mathematics
• 2007
We introduce the scale of weighted Bergman spaces on hyperconvex domains in C n and use the Lelong-Jensen formula to prove some fundamental results about these spaces. In particular, generalizations
Duality and approximation of Bergman spaces
• Mathematics
• 2019
The ring of holomorphic functions on a Stein compact set as a unique factorization domain
Let $\Gamma$ be the ring of germs of analytic functions on a Stein compact subset $K$ of a complex-analytic space. Necessary and sufficient conditions on $K$ for $\Gamma$ to be a unique
Dirichlet/Neumann problems and Hardy classes for the planar conductivity equation
• Mathematics
• 2011
We study Hardy spaces of the conjugate Beltrami equation over Dini-smooth finitely connected domains, for real contractive with , in the range . We develop a theory of conjugate functions and apply
Complex Analytic Sets
The theory of complex analytic sets is part of the modern geometric theory of functions of several complex variables. Traditionally, the presentation of the foundations of the theory of analytic sets
Boundary Behavior of Holomorphic Functions of Several Complex Variables.
This book has as its subject the boundary value theory of holomorphic functions in several complex variables, a topic that is just now coming to the forefront of mathematical analysis. For one
Boundary Behaviour of Conformal Maps
1. Some Basic Facts.- 2. Continuity and Prime Ends.- 3. Smoothness and Corners.- 4. Distortion.- 5. Quasidisks.- 6. Linear Measure.- 7. Smirnov and Lavrentiev Domains.- 8. Integral Means.- 9. Curve
SOLVING ∂ WITH PRESCRIBED SUPPORT ON HARTOGS TRIANGLES IN C 2 AND CP 2
In this paper, we consider the problem of solving the Cauchy– Riemann equation with prescribed support in a domain of a complex manifold for forms or currents. We are especially interested in the