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Let be the singular integral operator with variable kernel defined by and let be the fractional differentiation operator. Let and be the adjoint of and the pseudoadjoint of , respectively. In this paper, the authors prove that and are bounded, respectively, from Morrey-Herz spaces to the weak Morrey-Herz spaces by using the spherical harmonic decomposition. Furthermore, several norm inequalities for the product and the pseudoproduct are also given.

Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces