The commutators of multilinear fractional Calderón-Zygmund operators on weighted Hardy spaces

In this paper, we study the behaviors of the commutators [~b,T_γ] generated by multilinear fractional Calderón-Zygmund operators T_γ with vec b=(b_1,…,b_m)∈ (L_loc¹)^m on weighted Hardy spaces. Generally, for vec b∈ (BMO)^m, [~b,~T_γ] may be not bounded from the product Hardy spaces to Lebesgue spaces. We show that for some p_i∈(0,1 with 1/q=1/p_1+·s+1/p_m-γ/n, ωi∈ RH_q_i/p_iand b_i∈ mathcal BMOωi,p_i which are a class of non-trivial subspaces of rm BMO (bounded mean oscillation), i=1,…,m, the commutators [~b,T_γ] are bounded from H^p_1ω1