Multipliers between BMO Spaces on Open Unit Ball

BMO and VMO spaces consist of all those locally integrable functions on the open unit ball such that their mean oscillations on any Bergman ball are, respectively, bounded and vanishing to zero as the Bergman ball approaches the boundary of the unit ball. The harmonic (or analytic) versions of the BMO and VMO spaces are the Bloch space and the little Bloch space, respectively. The study of these spaces plays an important role in modern analysis, especially in the the area of operator theory and holomorphic spaces. In this paper, we characterize systematically the multipliers of BMO and VMO spaces.