A reproducing kernel thesis for operators on Bergman-type function   spaces
  In this paper we consider the reproducing kernel thesis for boundedness and compactness for various operators on Bergman-type spaces. In particular, the results in this paper apply to the weighted Bergman space on the unit ball, the unit polydisc and more generally to weighted Fock spaces. 
Mishko Mitkovski, Brett D. Wick
math.CV math.CA