We give a characterization of onto interpolating sequences with finite associated measure for the Dirichlet space in terms of condenser capacity. In the Sobolev space $H_1(\mathbb{D})$ we define a natural notion of onto interpolation and we prove that the same condenser capacity condition characterizes all onto interpolating sequences. As a result, for sequences with finite associated measure, the problem of interpolation by an analytic function reduces to a problem of interpolation by a function in $H_1(\mathbb{D})$.

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Dirichlet空间和 $H_{\mathrm{1个}}（\mathbb{d}）$

我们用电容器的容量对Dirichlet空间的有限相关度量给出插值序列的刻画。在Sobolev空间$H_{\mathrm{1个}}（\mathbb{d}）$我们定义了插值的自然概念，并证明了相同的电容器容量条件可将所有插值序列特征化。结果，对于具有有限关联度量的序列，通过解析函数进行插值的问题减少为通过函数进行插值的问题。$H_{\mathrm{1个}}（\mathbb{d}）$。