Abstract We introduce classes of pairs of weights closely related to Schrödinger operators, which allow us to get two-weight boundedness results for the Schrödinger fractional integral and its commutators. The techniques applied in the proofs strongly rely on one hand, boundedness results in the setting of finite measure spaces of homogeneous type and, on the other hand, Fefferman–Stein-type inequalities that connect maximal operators naturally associated to Schrödinger operators.

中文翻译：

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与薛定谔微分算子相关的极大算子的二加权不等式

摘要 我们引入了与薛定谔算子密切相关的权重对类，这使我们能够得到薛定谔分数积分及其对易子的二权重有界结果。证明中应用的技术一方面强烈依赖于有界性导致齐次类型的有限测度空间的设置，另一方面，Fefferman-Stein 型不等式连接了与薛定谔算子自然相关的最大算子。