Sharp multi‐weighted bounds for multilinear fractional rough operators and Cohen–Gosselin type commutators

In the article, we consider the multilinear fraction maximal operators and the multilinear fraction integrals with rough kernels, we introduce a new class for (m+1)‐weights tuple (u,ω⃗), and prove the optimal constant estimates of the sharp multi‐weighted bounds for both operators. We also show the sharp multi‐weighted bounds for the Cohen–Gosselin type multi‐commutator of the both operators.