On pointwise convergence of multilinear Bochner-Riesz means

We improve the range of indices when the multilinear Bochner-Riesz means converges pointwisely. We obtain this result by establishing the $L^p$ estimates and weighted estimates of $k$-linear maximal Bochner-Riesz operators inductively, which is new when $p<2\mathrm{/}k$ in higher dimensions. To prove these estimates, we make use of a variant of Stein’s square function and its multilinear generalization.