  In a celebrated conjecture D.Sarason stated a necessary and sufficient
condition on the symbols f, g in the Bergman space, L^2_a(\Delta) of the unit
disk, \Delta, for the products T_{f}T_{\bar g} of associated Toeplitz operators
to be bounded (respectively compact) on L^2_a(\Delta) . K. Stroethoff and D.
Zheng proved that these conditions are necessary. We prove the sufficiency of
these conditions, thus solvind Sarason's conjecture.
