Extension of Sobolev functions on balls in infinite dimensions

Abstract

We prove the existence of a bounded Sobolev extension operator $E:W^{p,1}\left(B,P\right)\to W^{p,1}\left({\ell }^2,P\right)$ using a completely new method, where $B\subset {\ell }^2$ is the unit ball and $P$ is any non-trivial centered Gaussian measure on ${\ell }^2$. This solves an open problem posed in the literatures.

arXiv commentThis manuscript has been withdrawn by the authors. It has been fully merged into arXiv:2602.04136v3. Please cite the merged paper instead