Weighted BMO and Hankel operators between Bergman spaces

Abstract

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 H f between weighted Bergman spaces.In particular, this resolves two questions left open in [7,12].