  In this paper, we construct coherent states for each generalized Bergman
space on the n-dimensional complex projective space in order to apply a
coherent states quantization method. Doing so allows to define the Berezin
transform for these spaces. In particular, we provide a variational formula for
this transform by means of the Fubini-Study Laplace operator which reduces when
n = 1 and for the lowest spherical Landau level to the well-known formula
previously given by Berezin himself.
