Boundedness of the bilinear Bochner-Riesz means in the non-Banach triangle case
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- by Heping Liu and Min Wang PDF
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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 $1\leq p_{1}=p_{2}<2$.References
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Additional Information
- Heping Liu
- Affiliation: School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
- MR Author ID: 262443
- 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
- 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
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 1121-1130
- MSC (2010): Primary 42B08; Secondary 42B15
- DOI: https://doi.org/10.1090/proc/14819
- MathSciNet review: 4055939