论文标题
关于公制空间中的Muckenhoupt重量的扩展
On the extension of Muckenhoupt weights in metric spaces
论文作者
论文摘要
沃尔夫（Wolff）的定理指出，在$ \ mathbb {r}^n $的可测量子集上定义的权重并满足Muckenhoupt型条件，可以将其扩展到整个空间中，因为同一类的Muckenhoupt权重。我们给出了该定理的完整且独立的证据，将其概括为支持加倍措施的度量措施空间。与扩展问题相关，我们还显示了公制设置中惠特尼链的Muckenhoupt重量的估计。
A theorem by Wolff states that weights defined on a measurable subset of $\mathbb{R}^n$ and satisfying a Muckenhoupt-type condition can be extended into the whole space as Muckenhoupt weights of the same class. We give a complete and self-contained proof of this theorem generalized into metric measure spaces supporting a doubling measure. Related to the extension problem, we also show estimates for Muckenhoupt weights on Whitney chains in the metric setting.
