Bilinear Bochner-Riesz square function and applications

Abstract

In this paper we introduce Stein's square function associated with bilinear Bochner-Riesz means and develop a systematic study of its $L^p$ boundedness properties. We also discuss applications of bilinear Bochner-Riesz square function in the context of bilinear fractional Schr\"{o}dinger multipliers, generalized bilinear spherical maximal function and more general bilinear multipliers defined on $\mathbb{R}^{2n}$ of the form $(\xi,\eta)\rightarrow m\left(|(\xi,\eta)|^2\right)$.Comment: Comments are welcom