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Maximal estimates for the bilinear spherical averages and the bilinear Bochner-Riesz operators (1903.07980v3)
Published 19 Mar 2019 in math.CA
Abstract: We study the maximal estimates for the bilinear spherical average and the bilinear Bochner-Riesz operator. Firstly, we obtain $Lp\times Lq \to Lr$ estimates for the bilinear spherical maximal function on the optimal range. Thus, we settle the problem which was previously considered by Geba, Greenleaf, Iosevich, Palsson and Sawyer, later Barrionevo, Grafakos, D. He, Honz\'ik and Oliveira, and recently Heo, Hong and Yang. Secondly, we consider $Lp\times Lq \to Lr$ estimates for the maximal bilinear Bochner-Riesz operators and improve the previous known results. For the purpose we draw a connection between the maximal estimates and the square function estimates for the classical Bochner-Riesz operators.