Extensions of Hilbert modules and Hankel operators

Extensions of the Hardy and the Bergman modules over the disc algebra. are studied. The author relates extensions of these canonical modules to the symbol spaces of corresponding Hankel operators. In the context of function theory, an explicit formula of Ext(L-a(2) (D), H-2(D)) is obtained. Finally, it is also proved that Ext(L-a(2)(D), L-a(2)(D)) not equal 0. This may be the essential difference between the Hardy and the Bergman modules over the disk algebra.