论文标题
无穷大的绿色功能应用于椭圆度测量的研究
The Green function with pole at infinity applied to the study of the elliptic measure
论文作者
论文摘要
在$ \ mathbb r^{d+1} _+$或$ \ mathbb r^n \ setminus \ mathbb r^d $（$ d <n-1 $）中，我们研究了大卫，恩格尔斯坦和梅博罗达引入的无限启动的绿色功能。在两种情况下，我们在$ \ Mathbb r^d $上推断出椭圆度度量与Lebesgue度量之间的等效性；而且，我们进一步证明了椭圆度度量的$ a_ \ infty $ -Absolute连续性，可以通过Carleson措施与之前的两个案例有关，从而扩展了$ a_ \ iffty $ ifty $ absolute连续性的操作员的范围。
In $\mathbb R^{d+1}_+$ or in $\mathbb R^n\setminus \mathbb R^d$ ($d<n-1$), we study the Green function with pole at infinity introduced by David, Engelstein, and Mayboroda. In two cases, we deduce the equivalence between the elliptic measure and the Lebesgue measure on $\mathbb R^d$; and we further prove the $A_\infty$-absolute continuity of the elliptic measure for operators that can be related to the two previous cases via Carleson measures, extending the range of operators for which the $A_\infty$-absolute continuity of the elliptic measure is known.
