Weighted Estimates of the Fractional Type Marcinkiewicz Integral and Its Commutator on Morrey–Guliyev Spaces

The aim of this paper is to study weighted estimates of the fractional type Marcinkiewicz integral and its commutator. By producing Guliyev type local pointwise estimates, we prove the boundedness of the fractional type Marcinkiewicz integral on the weighted Morrey–Guliyev spaces. Meanwhile, we also consider the corresponding weighted estimates of the commutators generated by a Lipschitz function and a BMO function.