Some estimates for multilinear Calderón-Zygmund operators with fractional kernels of Dini’s type and their commutators on generalized fractional mixed Morrey spaces

In this paper, we mainly study the boundedness of multilinear Calder?n-Zygmund operator with fractional kernel of type h(t) and its commutators on generalized fractional mixed Morrey space Lq⃗,η,ψ(R^n) . Firstly, with the help of the extrapolation theorem, the monotone convergence theorem and the boundedness of fractional integral operator I_ζ on mixed Lebesgue space Lq⃗(R^n) , we obtain the boundedness of T on space Lq⃗(R^n) . Secondly, the boundedness of T on space Lq⃗,η,ψ(R^n) is derived by applying the boundedness of T on space Lq⃗(R^n) . Thirdly, we prove that the commutators Tb⃗,1 and Tb⃗,2 are bounded from Lq⃗,η,ψ(R^n) × ⋯ × Lq⃗,η,ψ(R^n) to Lq⃗,η,ψ(R^n) . Finally, as applications, the boundedness for the multilinear fractional new maximal operator Mφ,β and its commutators Mb⃗,β and [b⃗, Mφ,β] on space Lq⃗,η,ψ(R^n) is presented.