The Harnack inequality for a class of nonlocal parabolic equations.

In this paper, we establish a scale invariant Harnack inequality for the fractional powers of parabolic operators (∂ t − ℒ) s , 0 < s < 1 , where ℒ is the infinitesimal generator of a class of symmetric semigroups. As a by-product, we also obtain a similar result for the nonlocal operators − ℒ s . Our focus is on non-Euclidean situations. [ABSTRACT FROM AUTHOR]