2017/03/27 by Zbigniew Błocki, Włodzimierz Zwonek, Błocki, Zbigniew +1
Mathematics · #30C85 #30H20 #32A36 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.1703.09297
openalex publication_date 2017/03/27 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
Carleson showed that the Bergman space for a domain on the plane is trivial\nif and only if its complement is polar. Here we give a quantitative version of\nthis result. One is the Suita conjecture, established by the first-named author\nin 2012, the other is an upper bound for the Bergman kernel in terms of\nlogarithmic capacity. We give some other estimates for those quantities as\nwell. We also show that the volume of sublevel sets for the Green function is\nnot convex for all regular non simply connected domains, generalizing a recent\nexample of Forn ae ss.\n