  Using the approach based on sesquilinear forms, we introduce Toeplitz
operator in the analytic Bergman space on the upper half-plane with strongly
singular symbols, derivatives of measures. Conditions for boundedness and
compactness of such operators are found. A procedure of reduction of Toeplitz
operators in Bergman spaces of polyanalytic functions to operators with
singular symbols in the analytic Bergman space by means of the
creation-annihilation structure is elaborated, which leads to the description
of the properties of the former operators
