On the bilinear Bochner-Riesz problem at critical index

Surjeet Singh Choudhary; Saurabh Shrivastava

paper

On the bilinear Bochner-Riesz problem at critical index

arXiv:2201.12036

Abstract

In this paper we study maximal and square functions associated with bilinear Bochner-Riesz means at the critical index. In particular, we prove that they satisfy weighted estimates from $L^{p_{1}} (w_{1}) \times L^{p_{2}} (w_{2}) \to L^{p} (v_{w})$ for bilinear weights $(w_{1}, w_{2}) \in A_{P}$ where $p_{1}, p_{2} > 1$ and $\frac{1}{p _{1}} + \frac{1}{p _{2}} = \frac{1}{p}$ . Also, we show that both the operators fail to satisfy weak-type estimates at the end-point $(1, 1, \frac{1}{2})$ .