The aim of this paper is to investigate the boundedness of a multilinear Calder? n-Zygmund integral operators with generalized kernels T and its commutator T₁ formed by b (BMO (Rⁿ) ) ᵐ and the T on product of generalized variable exponent Morrey spaces M^p₁ () ₁ (Rⁿ) M^p₂ () ₂ (Rⁿ) M^pₘ () ₘ (Rⁿ). Under assumption that the Lebesgue measurable satisfies ₁ ₂ ₘ =, the authors prove that the T is bounded from the product of generalized variable exponent Morrey spaces M^p₁ () ₁ (Rⁿ) M^p₂ () ₂ (Rⁿ) M^pₘ () ₘ (Rⁿ) to spaces M^p () (Rⁿ), and also bounded from the product variable exponent Morrey spaces L^p₁ () (Rⁿ) L^p₂ () ' (Rⁿ) L^pₘ () '' (Rⁿ) into spaces L^p () (Rⁿ). Moreover, the authors show that T₁ is bounded from the product spaces M^p₁ () ₁ (Rⁿ) M^p₂ () ₂ (Rⁿ) M^pₘ () ₘ (Rⁿ) to spaces M^p () (Rⁿ). As a corollary, the boundedness of T₁ on spaces L^p () (Rⁿ) is also obtained
Wang et al. (Wed,) studied this question.