The Bergman kernel and projection on non-smooth worm domains

By Steven G. Krantz, Marco M. Peloso. 2007

72 citations recorded by the source corpus.

This paper provides a precise asymptotic expansion for the Bergman kernel on the non-smooth worm domains of Christer Kiselman in complex 2-space. Applications are given to the failure of Condition R, to deviant boundary behavior of the kernel, and to L^p mapping properties of the kernel.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/210bb70a88a67ef3d7d2ed15afea83e9958d7976

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. L. Edholm
2. Jeffery D. McNeal
3. Yunus E. Zeytuncu
4. E. Straube
5. Siqi Fu

Citations in the corpus

• The Bergman projection on fat Hartogs triangles: L^p boundedness (2015, methodology): “of pas [1] shows for the Hartogs triangle. Earlier examples of restricted Lpmapping behavior of the Bergman projection on specific domains were given by Lanzani and Stein, [11], and Krantz and Peloso, [10]. The situation considered in this paper differs from that in [1] and [2] in one important respec”
• $L^p$ Regularity of Weighted Bergman Projections (2011, background): “ded non-pseudoconvex domain Din C2 such that the ordinary projection BD is not bounded on Lp(D) for p≥ 2+ 1 k where kis a positive integer depending on the domain. In a recent series of papers [KP07]-[KP08] Krantz and Peloso show that on the non-smooth worm domain Dβ ⊂ C2, the ordinary projection BD”
• Bergman Subspaces and Subkernels: Degenerate $$L^p$$Lp Mapping and Zeroes (2016, background): “Krantz and Peloso [16] showed that the Bergman projection on non-smooth versions of the worm domain has limited Lp boundedness.”
• The $L^p$ boundedness of the Bergman projection for a class of bounded Hartogs domains (2013, unknown): “[3], [12], [8], [11], [9], [10], [2], [6], etc.”