Weighted estimates for θ-type Calderón-Zygmund operator and its commutator on metric measure spaces

Abstract

Let be a non-homogeneous metric measure space satisfying the geometrically doubling condition and the upper doubling condition. In this setting, the author proves that the θ-type Calderón-Zygmund operator is bounded on the weighted Lebesgue space and the weighted Morrey space. Furthermore, the boundedness of the commutator generated by and on weighted weak Lebesgue space and on weighted weak Morrey space is also obtained.