On pointwise convergence of multilinear Bochner-Riesz means

TL;DR

This paper advances understanding of pointwise convergence of multilinear Bochner-Riesz means by establishing new $L^p$ and weighted estimates for associated maximal operators, especially in higher dimensions and for $p<2/k$.

Contribution

It introduces novel $L^p$ and weighted estimates for multilinear maximal Bochner-Riesz operators, extending convergence results to new index ranges and dimensions.

Findings

Improved range of indices for pointwise convergence.

Established $L^p$ estimates for multilinear maximal operators.

Developed a multilinear Stein's square function variant.

Abstract

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 $p<2/k$ in higher dimensions. To prove these estimates, we make use of a variant of Stein's square function and its multilinear generalization.