Multilinear Calderón-Zygmund integral operators with generalized kernels and their commutators on product of generalized variable exponent Morrey spaces

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 Tb⃗ formed by b⃗ ∈ (BMO(R^n))^m and the T on product of generalized variable exponent Morrey spaces Mp_1(·)φ_1(R^n) × Mp_2(·)φ_2(R^n) × ⋯ × Mp_m(·)φ_m(R^n). Under assumption that the Lebesgue measurable φ satisfies φ_1 φ_2 ⋯ φ_m = φ , the authors prove that the T is bounded from the product of generalized variable exponent Morrey spaces Mp_1(·)φ_1(R^n) × Mp_2(·)φ_2(R^n) × ⋯ × Mp_m(·)φ_m(R^n) to spaces Mp(·)φ(R^n) , and also bounded from the product variable exponent Morrey spaces Lp_1(·)λ(R^n) × Lp_2(·)λ'(R^n) × ⋯ × Lp_m(·)λ''(R^n) into spaces Lp(·)λ(R^n) . Moreover, the authors show that Tb⃗ is bounded from the product spaces Mp_1(·)φ_1(R^n) × Mp_2(·)φ_2(R^n) × ⋯ × Mp_m(·)φ_m(R^n) to spaces Mp(·)φ(R^n) . As a corollary, the boundedness of Tb⃗ on spaces Lp(·)λ(R^n) is also obtained