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

TL;DR

This paper studies the boundedness of bilinear Bochner-Riesz means in non-Banach spaces, offering a simpler partition of the non-Banach triangle and establishing lower smoothness indices for various cases beyond the equal p1 and p2 scenario.

Contribution

It introduces a simpler partition of the non-Banach triangle and derives lower smoothness indices for bilinear Bochner-Riesz means, improving upon previous results.

Findings

Simpler partition of the non-Banach triangle

Lower smoothness indices for various cases

Extended boundedness results beyond p1=p2<2

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 $1 \leq p_1=p_2 <2$.