Abstract: According to the definitions and properties of the weighted Lebesgue spaces and Herz spaces with variable exponent, using the property of variable index, and by the estimates of the Hlder inequalities, we proved the boundedness of the multilinear CalderónZygmund operators on the product of weighted Lebesgue spaces with variable exponent, and then proved the operators were bounded on the product of weighted Herz spaces with variable exponent.

Key words: Muckenhoupt weight, multilinear operator, singular integral operator, variable exponent, Herz space