The origin of the reduced electron heat diffusivity χe and the diffusion coefficient D in the core of H-mode plasmas is investigated. From the evolution of many local parameters in the L- and H-phases of ASDEX it follows that only the density scale length rn is a possible key parameter. The rn values are larger in the H-phase, but the electron temperature scale lengths remain unchanged. A local transport law for χe and D based on the increase of rn is tested by self-consistent transport simulations. It works for ASDEX H-mode discharges with edge localized modes, but is incompatible with the broad density profiles observed in other devices.