Let [Formula: see text] be a separable Banach space endowed with a nondegenerate centered Gaussian measure [Formula: see text] and let [Formula: see text] be a positive function on [Formula: see text] such that [Formula: see text] and [Formula: see text] for some [Formula: see text] and [Formula: see text]. In this paper, we introduce and study Sobolev spaces with respect to the weighted Gaussian measure [Formula: see text]. We obtain results regarding the divergence operator (i.e. the adjoint in [Formula: see text] of the gradient operator along the Cameron–Martin space) and the trace of Sobolev functions on hypersurfaces [Formula: see text], where [Formula: see text] is a suitable version of a Sobolev function.

中文翻译：

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关于无限维加权高斯测度的 Sobolev 空间

令 [Formula: see text] 为可分离 Banach 空间，赋予非退化中心高斯测度 [Formula: see text] 并令 [Formula: see text] 为 [Formula: see text] 上的正函数，使得 [Formula: see text] 和 [Formula: see text] 用于某些 [Formula: see text] 和 [Formula: see text]。在本文中，我们介绍和研究了关于加权高斯测度的 Sobolev 空间[公式：见正文]。我们获得了关于散度算子（即沿卡梅伦-马丁空间的梯度算子[公式：见文本]中的伴随）和超曲面上索博列夫函数的轨迹[公式：见文本]的结果，其中[公式：见文本] 是 Sobolev 函数的合适版本。