Hardy Spaces for a Class of Singular Domains

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.

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

References in corpus (1)

• The spectrum of the Leray transform for convex Reinhardt domains in ${\mathbb{C}}^2$

Cited by in corpus (2)

• Irregularity of the Bergman projection on smooth unbounded worm domains
• The Laplace and Leray transforms on some (weakly) convex domains in ${\mathbb{C}}^2$