Sobolev spaces of Wiener functionals and Malliavin's calculus (Q1068323)

Foundation of Malliavin's calculus. We studied the Sobolev spaces over an abstract Wiener space and discussed their properties, such as equivalence of several Sobolev type norms, continuity of the weak derivative operator and its dual operator, and so on. In particular, since our Sobolev spaces allow negative indices of differentiability, a distribution-like theory is available. As its application, we referred to Watanabe's approach to Malliavin's calculus in our framework.