On the Bilinear Bochner–Riesz Problem at Critical Index

In this paper, we study maximal and square functions associated with bilinear Bochner–Riesz means at the critical index. particular, prove that they satisfy weighted estimates from \(L^{p_1}(w_1)\times L^{p_2}(w_2)\rightarrow L^p(v_w)\) for weights \((w_1,w_2)\in A_{\textbf{P}}\) where \(p_1,p_2>1\) \(\frac{1}{p_1}+\frac{1}{p_2}=\frac{1}{p}\). Also, show both operators fail to weak-type end-point\(\big (1,1,\frac{1}{2}\big )\).