Two Weight Inequality for Hankel Form on Weighted Bergman Spaces Induced by Doubling Weights

The boundedness of the small Hankel operator induced by an analytic symbol f and the Bergman projectionPvassociated tov,acting from the weighted Bergman space

is characterized on the full range0 < p; q < ∞whenω , vbelong to the classDof radial weights admitting certain two-sided doubling conditions. Certain results obtained are equivalent to the boundedness of bilinear Hankel forms, which are in turn used to establish the weak factorization of the Bergman spaces.