Weighted estimates for some Schrödinger-type operators on spaces of homogeneous type

Let [Formula: see text] be a space of homogeneous type. Assume that [Formula: see text] satisfies the monotone geodesic property, then we prove some weighted estimates for Schrödinger-type operators, where the weights are Muckenhoupt-type weights associated with admissible functions modeled on the critical radius functions of Schrödinger operators. To be precise, we obtain the boundedness of the Schrödinger-type maximal Calderón–Zygmund operators on weighted [Formula: see text] with [Formula: see text] and from weighted [Formula: see text] to weighted [Formula: see text]. The same boundedness results extend to the Schrödinger-type Calderón–Zygmund operators as noted in prior work, though the rigorous proof remains absent; we provide the missing derivation in this study. The geometric properties associated with admissible functions and the dyadic cubes on [Formula: see text] play a crucial role in the proof of the results.