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We introduce new twisting techniques to establish new estimates for the minimal  L 2   solution of∂  ¯    $\bar{\partial }$    on weighted Bergman spaces in the unit ball. The estimate is used to obtain off-diagonal decay bounds for the associated Bergman kernel, and also improve sup-norm estimates obtained some time ago by Berndtsson.

journal für die reine und angewandte mathematik (crelles journal)

New estimates for the minimal  L 2   solution of        ∂  ¯    $\bar{\partial }$    and applications to geometric function theory in weighted Bergman spaces