Decay estimates, smoothing and hypocoercivity by adjoint and coupling methods

We describe a new approach, mostly based on adjoint and coupling methods, in order to give robust decay and smoothing estimates for a large class of Fokker-Planck equations, that include nonlocal and/or hypoelliptic diffusions. The purpose is to use structure conditions on the drift-diffusion terms, doubling variables and possibly time scaling, to avoid the explicit knowledge of fundamental solutions or functional inequalities.