Pointwise multipliers and corona type decomposition in $BMOA$

Abstract

In this paper we obtain several characterizations of the pointwise multipliers of the space BMOA 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 BMOA×...×BMOA onto BMOA if and only if the functions g j are multipliers of the space BMOA and satisfy ∑ j=1 m |g j (z)|≥δ>0.