Abstract for the talk on 22.11.2018 (11:00 h)
Arbeitsgemeinschaft ANGEWANDTE ANALYSISAlexander Shaposhnikov (Lomonosov Moscow State University)
Lusin-type theorems on the Wiener space
There are a number of classical results on the approximation of Sobolev functions
by Lipschitz continuous mappings on Euclidean spaces in the sense of Lusin,
as well as Lusin-type approximations of measurable vector fields by gradients of
Lipschitz-continuous functions. However, the classical proofs rely on the
doubling property of the Lebesgue measure and some other techniques
which are specific to the finite-dimensional setting.
Nevertheless, it turns out that for a infinite-dimensional space equipped with a Gaussian measure
there are natural counterparts of these results, although some questions remain open.
We will discuss some new observations in this area based on the estimates for heat semigroups
and some dimension-independent bounds.