Deformation quantization of a Kaehler-Poisson structure vanishing on a   Levi nondegenerate hypersurface
  We give an elementary proof of the result by Leichtnam, Tang, and Weinstein that there exists a deformation quantization with separation of variables on a complex manifold endowed with a Kaehler-Poisson structure vanishing on a Levi nondegenerate hypersurface and nondegenerate on its complement. 
Alexander V. Karabegov