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

Abstract

In this article, we investigate the boundedness of the bilinear Bochner-Riesz means $S^{\alpha }$ in the non-Banach triangle case. We improve the corresponding results in [Bern] in two aspects: Our partition of the non-Banach triangle is simpler and we obtain lower smoothness indices $\alpha (p_{1},p_{2})$ for various cases apart from $1 \leq p_1=p_2 <2$.