论文标题
双线性球形最大功能的稀疏边界
Sparse bounds for the bilinear spherical maximal function
论文作者
论文摘要
我们在任何维度$ d \ geq 1 $中得出双线性球形最大功能的稀疏界限。当$ d \ geq 2 $时，这立即将锋利的$ l^p \ times l^q \恢复到操作员绑定的l^r $，并暗示相对于双线性的毫无平衡的定量加权规范不平等，这似乎是操作员的第一个。关键创新是一组新开发的连续性$ l^p $改进单秤双线球形平均操作员的估计。
We derive sparse bounds for the bilinear spherical maximal function in any dimension $d\geq 1$. When $d\geq 2$, this immediately recovers the sharp $L^p\times L^q\to L^r$ bound of the operator and implies quantitative weighted norm inequalities with respect to bilinear Muckenhoupt weights, which seems to be the first of their kind for the operator. The key innovation is a group of newly developed continuity $L^p$ improving estimates for the single scale bilinear spherical averaging operator.
