Let [Formula: see text] be a separable Banach space endowed with a non-degenerate centered Gaussian measure [Formula: see text]. The associated Cameron–Martin space is denoted by [Formula: see text]. Consider two sufficiently regular convex functions [Formula: see text] and [Formula: see text]. We let [Formula: see text] and [Formula: see text]. In this paper, we study the domain of the self-adjoint operator associated with the quadratic form [Formula: see text] and we give sharp embedding results for it. In particular, we obtain a characterization of the domain of the Ornstein–Uhlenbeck operator in Hilbert space with [Formula: see text] and on half-spaces, namely if [Formula: see text] and [Formula: see text] is an affine function, then the domain of the operator defined via (0.1) is the space [Formula: see text] where [Formula: see text] is the Feyel–de La Pradelle Hausdorff–Gauss surface measure.

中文翻译：

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维纳空间集合上的椭圆算子域

令 [公式：见正文] 是一个可分离的 Banach 空间，具有非退化中心高斯测度 [公式：见正文]。相关的 Cameron-Martin 空间由 [公式：见正文] 表示。考虑两个足够规则的凸函数 [公式：参见文本] 和 [公式：参见文本]。我们让 [Formula: see text] 和 [Formula: see text]。在本文中，我们研究了与二次形式相关的自伴随算子的域[公式：见文本]，并给出了清晰的嵌入结果。特别是，我们在希尔伯特空间和半空间上获得了 Ornstein-Uhlenbeck 算子域的表征，即如果 [Formula: see text] 和 [Formula: see text] 是仿射的函数，则通过 (0.1) 定义的运算符的域是空间 [公式：见文本] 其中 [公式：