论文标题
在关键指数上的双线性bochner-riesz问题上
On the bilinear Bochner-Riesz problem at critical index
论文作者
论文摘要
在本文中，我们研究了与临界指数上与双线性Bochner-Riesz相关的最大和方形函数。特别是，我们证明它们满足了从$ l^{p_1}（w_1）\ times l^{p_2}（w_2）（w_2）\ rightArrow l^p（v_w）$的biinear weightege $（w_1，w_1，w_2）\ in _ _ _ { $ \ frac {1} {p_1}+\ frac {1} {p_2} = \ frac {1} {p} $。另外，我们表明，两个操作员都无法满足端点$（1,1，\ frac {1} {2}）$的弱类估计。
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 $L^{p_1}(w_1)\times L^{p_2}(w_2)\rightarrow L^p(v_w)$ for bilinear weights $(w_1,w_2)\in A_{\vec{P}}$ 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 $(1,1,\frac{1}{2})$.
