Higher-order commutators of the parameterized Marcinkiewicz integrals on central Morrey spaces with variable exponent

Abstract

By using the method of function decomposition on central Morrey spaces with variable exponent and with the help of the boundedness of Parametrized Marcinkiewicz integrals with rough kernels on $L^{p(\cdot)}(\mathbb{R}^{n})$, the boundedness of higher-order Lipschitz commutator and higher-order BMO commutator  of parameterized Marcinkiewicz integrals is estimated and obtained on central Morrey spaces with variable exponent.