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On the Bilinear Bochner–Riesz Problem at Critical Index

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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 \((w_1,w_2)\in A_{\textbf{P}}\) 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\(\big (1,1,\frac{1}{2}\big )\).

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Acknowledgements

Surjeet Singh Choudhary is supported by CSIR (NET), file no. 09/1020(0182)/2019-EMR-I. Saurabh Shrivastava acknowledges the support from Science and Engineering Research Board, Department of Science and Technology, Govt. of India, under the scheme Core Research Grant with file no. CRG/2021/000230.

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  1. Department of Mathematics, Indian Institute Science Education and Research Bhopal, Bhopal, 462066, India

    Surjeet Singh Choudhary & Saurabh Shrivastava

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  1. Surjeet Singh Choudhary
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  2. Saurabh Shrivastava
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Correspondence to Saurabh Shrivastava.

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Choudhary, S.S., Shrivastava, S. On the Bilinear Bochner–Riesz Problem at Critical Index. J Geom Anal 33, 58 (2023). https://doi.org/10.1007/s12220-022-01122-8

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