Maximal estimates for bilinear Bochner-Riesz means

Abstract

We establish improved Lp estimates for the maximal bilinear Bochner-Riesz means in all dimensions n ≥ 1. This work extends the results proved by Jeong and Lee [11]. 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 − |ξ|2 − |η|2)α+and delicate analysis in proving Lp estimates for frequency localised square functions.