Graham type theorem on classical bounded symmetric domains

摘要

Graham Theorem on the unit ball B-n in C-n states that every invariant harmonic function u is an element of C-n((B) over bar (n)) must be pluriharmonic in B-n (Graham in Commun Partial Differ Equ 8(5):433-476, 1983). This rigidity phenomenon of Graham has been studied by many authors [see, for examples, Graham and Lee (Duke Math J 57:697-720, 1988), Li and Simon (Am J Math 124:1045-1057, 2002), Li and Wei (Sci China Math 53:779-790, 2010), etc]. In this paper, we prove that Graham theorem holds on classical bounded symmetric domains, which include Type I and Type II domains, Type III domain III(n) and Type IV domain IV(n) with even n >= 4.