In the setting of the semigroup generated by the Schrödinger operator \(L= -\Delta +V\) with the potential V satisfying an appropriate reverse Hölder condition, we consider some non-local fractional differentiation operators. We study their behaviour on suitable weighted smoothness spaces. Actually, we obtain such continuity results for positive powers of L as well as for the mixed operators \(L^{\alpha /2}V^{\sigma /2}\) and \(L^{-\alpha /2}V^{\sigma /2}\) with \(\sigma >\alpha \), together with their adjoints.

中文翻译：

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Schrödinger算子在Lipschitz空间上的分数次幂

在由薛定ding算子\（L =-\ Delta + V \）生成的半群的设置中，势V满足适当的逆Hölder条件，我们考虑了一些非局部分数阶微分算子。我们在合适的加权平滑空间上研究它们的行为。实际上，对于L的正幂以及混合算符\（L ^ {\ alpha / 2} V ^ {\ sigma / 2} \）和\（L ^ {-\ alpha / 2 } V ^ {\ sigma / 2} \）与\（\ sigma> \ alpha \）以及它们的伴随项。