Multilinear estimates for maximal rough singular integrals

In this work, we establish Lp₁× ⋯× Lp₁→ Lᵖ bounds for maximal multi-(sub)linear singular integrals associated with homogeneous kernels Ω(y⃗')|y⃗|ᵐⁿ where Ω is an Lq function on the unit sphere Sᵐⁿ⁻¹ with vanishing moment condition and $q>1$. As an application, we obtain almost everywhere convergence results for the associated doubly truncated multilinear singular integrals.