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Boundedness of the bilinear Bochner-Riesz means in the non-Banach triangle case


Authors: Heping Liu and Min Wang
Journal: Proc. Amer. Math. Soc. 148 (2020), 1121-1130
MSC (2010): Primary 42B08; Secondary 42B15
DOI: https://doi.org/10.1090/proc/14819
Published electronically: November 19, 2019
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Abstract: In this article, we investigate the boundedness of the bilinear Bochner-Riesz means $ B^{\alpha }$ in the non-Banach triangle case. Bernicot et al. studied the bilinear Bochner-Riesz problem for $ n\geq 2$. Jeong, Lee, and Vargas improved their results in the Banach triangle case. We shall improve their results in the non-Banach triangle case. Improvement is reflected in two aspects: our partition of the non-Banach triangle is simpler; we obtain lower smoothness indices $ \alpha (p_{1},p_{2})$ for various cases apart from $ 1\leq p_{1}=p_{2}<2$.


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Additional Information

Heping Liu
Affiliation: School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
Email: hpliu@math.pku.edu.cn

Min Wang
Affiliation: School of Mathematical Sciences, Fudan University, Shanghai 200433, People’s Republic of China
Email: wangmin09150102@163.com

DOI: https://doi.org/10.1090/proc/14819
Keywords: Bilinear Bochner-Riesz means, restriction theorem
Received by editor(s): December 2, 2018
Received by editor(s) in revised form: June 24, 2019
Published electronically: November 19, 2019
Additional Notes: The first author was supported by NNSFC Grant #11371036
The second author was supported by CSC Grant #201606010026
The second author is the corresponding author
Communicated by: Svitlana Mayboroda
Article copyright: © Copyright 2019 American Mathematical Society