Pointwise multipliers and corona type decomposition in B M O A

In this paper we obtain several characterizations of the pointwise multipliers of the space B M O A in the unit ball B of ℂ n . Moreover, if g 1 , ... , g m are holomorphic functions on B , we prove that M g ( f ) ( z ) = ∑ j = 1 m g j ( z ) f j ( z ) maps B M O A × ... × B M O A onto B M O A if and only if the functions g j are multipliers of the space B M O A and satisfy ∑ j = 1 m | g j ( z ) | ≥ δ > 0 .