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 −ℒs. Our focus is on non-Euclidean situations.

中文翻译：

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一类非局部抛物方程的哈纳克不等式

在本文中，我们为抛物线算子的分数幂建立了尺度不变的 Harnack 不等式(∂吨 -ℒ)s,0 < s < 1， 在哪里ℒ是一类对称半群的无穷小生成元。作为副产品，我们也为非本地算子获得了类似的结果 -ℒs. 我们的重点是非欧几里得情况。