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

Liu, Heping; Wang, Min

doi:10.1090/proc/14819

Boundedness of the bilinear Bochner-Riesz means in the non-Banach triangle case
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by Heping Liu and Min Wang PDF

Proc. Amer. Math. Soc. 148 (2020), 1121-1130 Request permission

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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