The domain of definition of the quaternionic Monge–Ampère operator

Abstract

In this paper, we give an equivalent characterization of the domain of definition for the quaternionic Monge-Ampère operator, by using the theory of quaternionic closed positive current we established in [17][18][19]. This domain of definition for the complex Monge-Ampère operator was introduced by Blocki [7,8]. K E Y W O R D S Monge-Ampère operator, positive current, quaternionic plurisubharmonic function M S C ( 2 0 1 0 ) 31C10, 32U15, 32U40].Alesker proved in [4] a quaternionic version of Chern-Levine-Nirenberg estimate and extended the definition of quaternionic Monge-Ampère operator to continuous quaternionic plurisubharmonic functions. Since it is inconvenient to use the Moore