6 papers
On the equivalence of Sobolev norms in infinite dimensions
Zhouzhe Wang
We prove dimension-free higher-order Sobolev norm estimates on open convex subsets of with respect to Gaussian measure and use them to obtain norm equivalence on non…
Measures on General Codimensional Surfaces in Infinite Dimensions and Stokes-Type Theorems
Zhouzhe Wang, Jiayang Yu, Xu Zhang
In this paper, we give an explicit construction of surface measures on a class of surfaces with arbitrary, possibly infinite, codimension in . These measures are constructe…
Extension of Sobolev functions on balls in infinite dimensions
Zhouzhe Wang, Xu Zhang, Shiliang Zhao
We prove the existence of a bounded Sobolev extension operator using a completely new method, where $B\s…
Sobolev spaces in infinite dimensions
Zhouzhe Wang, Jiayang Yu, Xu Zhang +2
The classical theory of Sobolev spaces in finite dimensions is well established. Because infinite-dimensional spaces possess inherent analytical and topological complexities, devel…
Smooth plurisubharmonic exhaustion functions on pseudo-convex domains in infinite dimensions
Zhouzhe Wang, Xu Zhang
In this paper, by modifying significantly the Friedrichs-Gross mollifier technique and/or using the Lasry-Lions regularization technique together with some carefully chosen cut-off…
estimates and existence theorems for the operators in infinite dimensions, II
Zhouzhe Wang, Jiayang Yu, Xu Zhang
This paper is the second part of our series of works to establish estimates and existence theorems for the operators in infinite dimensions. In this par…