Some estimates of multi-sublinear operators and commutators on mixed λ -central Morrey spaces

In this paper, we establish the boundedness of multi-sublinear operators 𝒯_m, 𝒯_α ,m, multi-sublinear commutators 𝒯^b⃗_m, 𝒯^b⃗_α ,m and iterated commutators 𝒯^Πb⃗_m, 𝒯^Πb⃗_α ,m generated with mixed λ -central BMO functions b⃗ on mixed λ -central Morrey spaces ℬ^q⃗,λ(ℝ^n), respectively, where b⃗=(b_1,… ,b_m), q⃗=(q_1,… ,q_m) and b_i∈CBMO^q⃗_⃗i⃗,λ _i(ℝ^n) for i=1,2,… ,m. Similar results still hold for multilinear maximal operators T^*, their commutators T^*_b⃗ and T^*_Πb⃗. In addition, we also derive the boundedness of multilinear commutators I^*_α ,b⃗ of multilinear fractional maximal operators I^*_α on mixed λ -central Morrey spaces ℬ^q⃗,λ(ℝ^n). As applications, we obtain the boundedness of the multilinear Calderón–Zygmund operators T_m, multilinear fractional operators T_α ,m and their commutators generated with mixed λ -central BMO functions on mixed λ -central Morrey spaces ℬ^q⃗,λ(ℝ^n), respectively.