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arXiv · 2203.13303

Sparse bounds for the bilinear spherical maximal function

Tainara Borges·Benjamin Foster·Yumeng Ou·Jill Pipher·Zirui Zhou
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Abstract

We derive sparse bounds for the bilinear spherical maximal function in any dimension $d\geq 1$. When $d\geq 2$, this immediately recovers the sharp $L^p\times L^q\to L^r$ bound of the operator and implies quantitative weighted norm inequalities with respect to bilinear Muckenhoupt weights, which seems to be the first of their kind for the operator. The key innovation is a group of newly developed continuity $L^p$ improving estimates for the single scale bilinear spherical averaging operator.

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Tainara Borges, Benjamin Foster, Yumeng Ou, Jill Pipher, Zirui Zhou. 2022-03-24. Sparse bounds for the bilinear spherical maximal function. https://arxiv.org/abs/2203.13303

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