Gross-Stroock Sobolev Spaces over a Gaussian Probability Space

Abstract

Continuity of the Cameron-Martin representation over L^∞−0 — The space D ^∞₁ of differentiable vectors of the Cameron-Martin representation — Gradient operator — Generalized polynomials — Cauchy operator; Krée-Meyer inequality for the gradient — The spaces D ^p₁ — Gradient of Hilbert-valued functionals — Recursive approach to higher derivatives and to Krée-Meyer inequalities of higher order — The space D_∞ of smooth functionals, its approximation by C^∞ cylindrical functionals — Divergence as the adjoint of the gradient — Divergence of smooth vector fields — Shigekawa acyclicity of the complex of differential forms — Appendix: Proof of the L^p inequality for the Hilbert transform.