On pointwise convergence of multilinear Bochner-Riesz means

2024/11/30 by He, Danqing, Li, Kangwei, Zheng, Jiqiang
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.00296

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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