Boundedness Criterion for Multi-sublinear Operators and Their Commutators Generated by Multilinear Fractional Integral Operator on Product Generalized Mixed Morrey Spaces

The purpose of this paper is to study the boundedness for a large class of multi-sublinear operators T α,m generated by multilinear fractional integral operator and their commutators T_α ,m,i^b (i = 1, … m) on product generalized mixed Morrey spaces M_q_1^φ _1(ℝ^n) ×⋯× M_q_m^φ _m(ℝ^n) . We find sufficient conditions on ( ϕ 1 , …, ϕ m , ϕ ) which ensure the boundedness of T α,m from M_q_1^φ _1(ℝ^n) ×⋯× M_q_m^φ _m(ℝ^n) to M_p⃗^φ (ℝ^n) . Moreover, we also give sufficient conditions for the boundedness of T α,m,i from M_q_1^φ _1(ℝ^n) ×⋯× M_q_m^φ _m(ℝ^n) to M_p⃗^φ (ℝ^n) . As applications, the boundedness for multi-sublinear fractional maximal operator, multilinear fractional integral operator and their commutators on product generalized mixed Morrey spaces is established.