Cauchy transforms and Szegő projections in dual Hardy spaces: inequalities and Möbius invariance
arXiv:2407.13033 · doi:10.1016/j.jfa.2025.110980
Abstract
Dual pairs of interior and exterior Hardy spaces associated to a simple closed Lipschitz planar curve are considered, leading to a Möbius invariant function bounding the norm of the Cauchy transform from below. This function is shown to satisfy strong rigidity properties and is closely connected via the Berezin transform to the square of the Kerzman-Stein operator. Explicit example calculations are presented. For ellipses, a new asymptotically sharp lower bound on the norm of is produced.
28 pages, 3 figures