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arXiv · 2412.00296

On pointwise convergence of multilinear Bochner-Riesz means

Danqing He·Kangwei Li·Jiqiang Zheng
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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.

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Danqing He, Kangwei Li, Jiqiang Zheng. 2024-11-30. On pointwise convergence of multilinear Bochner-Riesz means. https://arxiv.org/abs/2412.00296

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