In this paper,we investigate what are Carleson measures on open subsets in the complex plane.A circular domain is a connected open subset whose boundary consists of finitely many disjoint circles.We call a domain G mu...In this paper,we investigate what are Carleson measures on open subsets in the complex plane.A circular domain is a connected open subset whose boundary consists of finitely many disjoint circles.We call a domain G multi-nicely connected if there exists a circular domain W and a conformal mapψfrom W onto G such thatψis almost univalent with respect the arclength onδW.We characterize all Carleson measures for those open subsets so that each of their components is multinicely connected and harmonic measures of the components are mutually singular.Our results suggest the extension of Carleson measures probably is up to this class of open subsets.展开更多
文摘In this paper,we investigate what are Carleson measures on open subsets in the complex plane.A circular domain is a connected open subset whose boundary consists of finitely many disjoint circles.We call a domain G multi-nicely connected if there exists a circular domain W and a conformal mapψfrom W onto G such thatψis almost univalent with respect the arclength onδW.We characterize all Carleson measures for those open subsets so that each of their components is multinicely connected and harmonic measures of the components are mutually singular.Our results suggest the extension of Carleson measures probably is up to this class of open subsets.
