  We consider the well-posedness of the initial value problem associated to the
k-generalized Zakharov-Kuznetsov equation in fractional weighted Sobolev
spaces. Our method of proof is based on the contraction mapping principle and
it mainly relies on the well-posedness results recently obtained for this
equation in the Sobolev spaces H^s(\R^2) and a new pointwise commutator type
formula involving the group induced by the linear part of the equation and the
fractional anisotropic weights to be considered
