Weighted BMO and Hankel Operators Between Bergman Spaces

We introduce a family of weighted BMO spaces in the Bergman metric on the unit ball of C-n, and use them to characterize complex functions f such that the big Hankel operators H-f and H-f(-) are both bounded or compact from a weighted Bergman space into a weighted Lesbegue space with possibly different exponents and different weights. As a consequence, when the symbol function f is holomorphic, we characterize bounded and compact Hankel operators Hf between weighted Bergman spaces. In particular, this resolves two questions left open in [7,12].