2024/07/17 by David E. Barrett, Barrett, David E., Luke D. Edholm +1
Mathematics · #30C40 (Primary) #30E20 #30H10 #32A25 #46E22 (Secondary) #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2407.13033
openalex publication_date 2024/07/17 · openalex created_date 2025/01/04 · openalex updated_date 2026/07/28
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 \bfC 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 \bfC is produced.