Zhouzhe Wang

On the equivalence of Sobolev norms in infinite dimensions

We prove dimension-free higher-order Sobolev norm estimates on open convex subsets of $\mathbb{R}^n$ with respect to Gaussian measure and use them to obtain norm equivalence on nonempty open convex subsets of $\ell^2$ endowed with a nondegenerate Gaussian measure. To the best of our knowledge, this is the first such eq...