The Leray transform
- Author(s)
- Luke David Edholm, David Barrett
- Abstract
We compute the exact norms of the Leray transforms for a family S
β of unbounded hypersurfaces in two complex dimensions. The S
β generalize the Heisenberg group, and provide local projective approximations to any smooth, strongly C-convex hypersurface S to two orders of tangency. This work is then examined in the context of projective dual CR-structures and the corresponding pair of canonical dual Hardy spaces associated to S, leading to a universal description of the Leray transform and a factorization of the transform through orthogonal projection onto the conjugate dual Hardy space.
- Organisation(s)
- Department of Mathematics
- External organisation(s)
- University of Michigan
- Journal
- Advances in Mathematics
- Volume
- 364
- No. of pages
- 42
- ISSN
- 0001-8708
- DOI
- https://doi.org/10.1016/j.aim.2020.107012
- Publication date
- 04-2020
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101008 Complex analysis
- Keywords
- ASJC Scopus subject areas
- Mathematics(all)
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/the-leray-transform(9ff2056b-a301-4e6b-92e9-06982128be4f).html