2024/10/17 by Bartosz Malman, Malman, Bartosz, Daniel Seco +1
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Primary 30H45 #Secondary 47B32
paper · pdf · doi:10.48550/arxiv.2410.13438
openalex publication_date 2024/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
To every non-extreme point b of the unit ball of \hil^∞ of the unit disk there corresponds a Pythagorean mate, a bounded outer function a satisfying the equation |a|2 + |b|2 = 1 on the boundary of the disk. We study universal, i.e., simultaneous multipliers for families of de Branges-Rovnyak spaces \hb, and develop a general framework for this purpose. Our main results include a new proof of the Davis-McCarthy universal multiplier theorem for the class of all non-extreme spaces \hb, a characterization of the Lipschitz classes as the universal multipliers for spaces \hb for which the quotient b/a is contained in a Hardy space, and a similar characterization of the Gevrey classes as the universal multipliers for spaces \hb for which b/a is contained in a Privalov class.