Compactness of products of Hankel operators on convex Reinhardt domains   in C^2
  Let D be a piecewise smooth bounded convex Reinhardt domain in C^2. Assume that the symbols f and g are continuous on the closure of D and harmonic on the disks in the boundary of D. We show that if the product of Hankel operators H^*_f H_g is compact on the Bergman space of D, then on any disk in the boundary of D, either f or g is holomorphic. 
Zeljko Cuckovic and Sonmez Sahutoglu
math.CV math.FA