Toeplitz operators defined by sesquilinear forms: Bergman space case
  The definition of Toeplitz operators in the Bergman space $A^2(D)$ of square integrable analytic functions in the unit disk in the complex plane is extended in such way that it covers many cases where the traditional definition does not work. This includes, in particular, highly singular symbols such as measures, distributions, and certain hyper-functions. 
Grigori Rozenblum, Nikolai Vasilevski
math.CV math.FA