$A_p$-$A_{\mathrm{\infty }}$ estimates for general multilinear sparse operators

In this paper, we study the $A_p$-$A_{\mathrm{\infty }}$ estimates for a class of multilinear dyadic positive operators. As applications, the $A_p$-$A_{\mathrm{\infty }}$ estimates for different operators e.g. multilinear square functions and multilinear Fourier multipliers can be deduced very easily.