论文标题
在迪里奇特类型的空间中完全无效和容量
Totally null sets and capacity in Dirichlet type spaces
论文作者
论文摘要
在$ \ mathbb {C}^d $的单位球上的Dirichlet类型空间的背景下，也称为Hardy-Sobolev或Besov-Sobolev空间，我们比较了单位球体紧凑子集的两个小概念。我们表明，完全无效的功能分析概念与容量为零的潜在理论概念一致。特别是，这适用于设备盘和对数容量上的经典迪里奇集团空间。结合戴维森（Davidson）和第二名作者的峰值插值结果，我们获得了佩勒（Peller）和赫鲁什奇夫（Khrushchëv）以及科恩（Cohn and verbitsky）的边界插值定理的增强。
In the context of Dirichlet type spaces on the unit ball of $\mathbb{C}^d$, also known as Hardy-Sobolev or Besov-Sobolev spaces, we compare two notions of smallness for compact subsets of the unit sphere. We show that the functional analytic notion of being totally null agrees with the potential theoretic notion of having capacity zero. In particular, this applies to the classical Dirichlet space on the unit disc and logarithmic capacity. In combination with a peak interpolation result of Davidson and the second named author, we obtain strengthenings of boundary interpolation theorems of Peller and Khrushchëv and of Cohn and Verbitsky.
