Abstract
In this paper, we establish a scale invariant Harnack inequality for the fractional powers of parabolic operators [Formula: see text], [Formula: see text], where [Formula: see text] is the infinitesimal generator of a class of symmetric semigroups. As a by-product, we also obtain a similar result for the nonlocal operators [Formula: see text]. Our focus is on non-Euclidean situations.
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