Kähler diffusions, carleson measures and BMOA functions of several complex variables

Abstract

In this paper we give some characterizations of BMOA functions in terms of Kahler diffusions and Carleson measures on the unit ball in C n n1 (see Theorem 1). This result implies Carleson measure characterizations of BMOA obtained recently by Choa and Choe [2] and Stanton [19]. Furthermore, as a corollary we prove that the spaces BMOA and BMO are isomorphic to closed complemented subspaces of a space of BMO martingales. From this it follows a non-isotropic version of Garnett-Jones theorem.