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On the Bochner-Riesz operator in ℝ3

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Abstract

We improve the Bochner-Riesz conjecture in ℝ3 to

$$\max \left\{ {p,p/\left( {p - 1} \right)} \right\} \ge 3.25.$$

Our main methods are the Bourgain—Guth broad-narrow argument and Guth’s polynomial partitioning iteration. The main novelty of this paper is a backward algorithm that emerges from the iteration we used. This algorithm helps us realize a geometric observation from the tangential contributions.

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Acknowlegement

I would like to thank my advisor Xiaochun Li for his encouragements throughout the project. I would also like to thank Mengzhudong Feng and Jiahao Hu for helpful discussions related to algebraic geometry.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Shukun Wu

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  1. Shukun Wu
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Correspondence to Shukun Wu.

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Wu, S. On the Bochner-Riesz operator in ℝ3. JAMA 149, 677–718 (2023). https://doi.org/10.1007/s11854-022-0263-y

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  • DOI: https://doi.org/10.1007/s11854-022-0263-y

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