Higer-order commutators of parametrized Marcinkewicz integrals on Herz spaces with variable exponent

Let 0<ρ<n and μ ρ Ω be the Parametrized Marcinkiewicz integrals operator. In this work, the bondedness of μ ρ Ω is discussed on Herz spaces ˙ K α,q(⋅) p(⋅) (Rn), where the two main indices are variable exponent. The boundedness of the commutators generated by BOM function, Lipschitz function and parametrized Marcinkiewicz integrals operator is also discussed.