Maximal estimates for bilinear Bochner-Riesz means

We establish improved and sharp $L^p$ estimates for the maximal bilinear Bochner-Riesz means in all dimensions $n\geq 1$. This work extends the results proved by Jeong and Lee \cite{JL}. We also recover the known results for the bilinear Bochner-Riesz means. The method of proof involves a new decomposition of the bilinear Bochner-Riesz multiplier $(1-|\xi|^2-|\eta|^2)_+^{\alpha}$ and delicate analysis in proving $L^p$ estimates for frequency localized square functions.