Abstract
We compute the exact norms of the Leray transforms for a family Sβ of unbounded hypersurfaces in two complex dimensions. The Sβ 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.
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