Harmonic majoration of quasibounded type

Shigeo Segawa

Vol. 84 (1979), No. 1, 199–200

DOI: 10.2140/pjm.1979.84.199

Abstract

Let O_AL (resp. O_AS) be the class of open Riemann surfaces on which there exists no nonconstant analytic functions f such that log ⁺|f| have harmonic (resp. quasi-bounded harmonic) majorant. It is shown that O_AL = O_AS for surfaces of finite genus.

Mathematical Subject Classification 2000

Primary: 30F20

Milestones

Received: 9 February 1979

Published: 1 September 1979