PreprintCC0arXiv
Extension of Sobolev functions on balls in infinite dimensions
Abstract
We prove the existence of a bounded Sobolev extension operator E:Wp,1( B,P ) → Wp,1( ℓ2 ,P ) using a completely new method, where B⊂ ℓ2 is the unit ball and P is any non-trivial centered Gaussian measure on ℓ2. This solves an open problem posed in the literatures.
Related
- On the equivalence of Sobolev norms in infinite dimensions
- Explicit Robin Green's Functions and Resonance Spectra for the Helmholtz Equation on Balls in All Dimensions
- Scalar--Mean Rigidity for Hyperbolic Balls in Dimensions 2≤ n≤ 5
- On the measure of the boundary of a Hajłasz-Sobolev (M1,p,M1,q)-extension domain
- Dimension-free estimates for full discrete maximal functions associated with Euclidean balls and spheres
BibTeX
@misc{wang2026extension,
title = {{Extension of Sobolev functions on balls in infinite dimensions}},
author = {Zhouzhe Wang and Xu Zhang and Shiliang Zhao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.06229},
eprint = {2606.06229},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.06229},
note = {CC0},
}
RIS
TY - UNPB
TI - Extension of Sobolev functions on balls in infinite dimensions
AU - Zhouzhe Wang
AU - Xu Zhang
AU - Shiliang Zhao
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2606.06229
UR - https://arxiv.org/abs/2606.06229
AB - We prove the existence of a bounded Sobolev extension operator E:W^p,1( B,P ) → W^p,1( ℓ^2 ,P ) using a completely new method, where B⊂ ℓ^2 is the unit ball and P is any non-trivial centered Gaussian measure on ℓ^2. This solves an open problem posed in the literatures.
ER -