  We investigate a non-homogeneous nonlinear heat equation which involves
degenerate or singular coefficients belonging to the $A_2$ class of functions.
We prove the existence of a Fujita exponent and describe the dichotomy
existence/non-existence of global in time solutions. The $A_2$ coefficient
admits either a singularity at the origin or a line of singularities. In this
latter case, the problem is related to the fractional laplacian, through the
Caffarelli-Silvestre extension and is a first attempt to develop a parabolic
theory in this setting.
