Multilinear estimates for maximal rough singular integrals

Abstract

In this work, we establish $L^{p_1}\times \cdots \times L^{p_m}\to L^p$ bounds for maximal multi-(sub)linear singular integrals associated with homogeneous kernels $\frac{\hat{I}\text{c◯}({\vec{\mathbf{y}}}^{\prime })}{|\vec{\mathbf{y}}{|}^{mn}}$ where $\hat{I}\text{c◯}$ is an $L^q$ function on the unit sphere ${\mathbb{S}}^{mn-1}$ with vanishing moment condition and $q>1$. As an application, we obtain almost everywhere convergence results for the associated doubly truncated multilinear singular integrals.

Typos have been corrected