About the convergence to initial data of the heat problem on the Heisenberg group

We find integrability conditions on the initial data $f$ for the existence of solutions of the Heat problem on the Heisenberg group. From this result we characterize the weighted Lebesgue spaces for which the solutions exists a.e. when the time goes to zero. Finally we also obtain boundedness of the local maximal function associated to the heat kernel with weights.