On Bilinear Maximal Bochner-Riesz Operators

We prove that the bilinear maximal Bochner-Riesz operator $T_{\ast }^{\lambda }$ is bounded from $L^{p_1}({\mathbb{R}}^n)\times L^{p_2}({\mathbb{R}}^n)$ to $L^p(\mathbb R^n)$forappropriate$(p_1,p_2,p)$when$\lambda>(4n+3)/5$.