Gross-Stroock Sobolev Spaces over a Gaussian Probability Space

  • Paul Malliavin
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 313)


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 1 p — 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.


Bilinear Form Differential Form Cauchy Sequence Separable Hilbert Space Hermite Polynomial 
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© Springer-Verlag Berlin Heidelberg 1997

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  • Paul Malliavin

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