# 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
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