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Our aim in this paper is to give the boundedness of the Marcinkiewicz integral μΩ on Herz spaces K˙p(·)α(·),q(Rn) and Kp(·)α(·),q(Rn), where the two main indices are variable. Meanwhile, we consider the boundedness of the higher order commutator μΩ,bm generated by μΩ and a function b in BMO(Rn) on these spaces.

Marcinkiewicz Integral Operators and Commutators on Herz Spaces with Variable Exponents