Harnack's Inequality and A Priori Estimates for Fractional Powers of   Non-symmetric Differential Operators
  We obtain a new general extension theorem in Banach spaces for operators which are not required to be symmetric, and apply it to obtain Harnack estimates and a priori regularity for solutions of fractional powers of several second order differential operators. These include weighted elliptic and subellitptic operators in divergence form (nonnecessarily self-adjoint), and nondivergence form operators with rough coefficients. We utilize the reflection extension technique introduced by Caffarelli and Silvestre. 
Hugo Aimar, Gast\'on Beltritti, Ivana G\'omez, Cristian Rios
math.AP