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arXiv · 2201.12036

On the bilinear Bochner-Riesz problem at critical index

Surjeet Singh Choudhary·Saurabh Shrivastava
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Abstract

In this paper we study maximal and square functions associated with bilinear Bochner-Riesz means at the critical index. In particular, we prove that they satisfy weighted estimates from $L^{p_1}(w_1)\times L^{p_2}(w_2)\rightarrow L^p(v_w)$ for bilinear weights $(w_1,w_2)\in A_{\vec{P}}$ where $p_1,p_2>1$ and $\frac{1}{p_1}+\frac{1}{p_2}=\frac{1}{p}$. Also, we show that both the operators fail to satisfy weak-type estimates at the end-point $(1,1,\frac{1}{2})$.

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Surjeet Singh Choudhary, Saurabh Shrivastava. 2022-01-28. On the bilinear Bochner-Riesz problem at critical index. https://arxiv.org/abs/2201.12036

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