Siberian Federal University

Study was started in [1,2] of the normed spaces of multiplicative holomorphic automorphic forms for a Fuchsian group. In the present article bilinear pairings for general duality of the (q,p)-forms are considered. The symmetric variant of bilinear pairing which can be used in the theory of single-valued automorphic forms is received. On the basis of the entered bilinear pairings the modified integral Bers operators corresponding to them are investigated. These operators relate to a reflection in some quasicircle and also are connected to the general duality of (q,p)-forms. Under study the universal norm estimates for all operators is received.