Year: 2025
Type: article
Abstract: The goal of this note is to prove that every real-valued Lipschitz function on a Banach space can be pointwise approximated on a given $$\sigma $$ σ -compact set by smooth cylindrical functions whose asymptotic Lipschitz constants are controlled. This result has applications in the study of metric Sobolev and BV spaces: it implies that smooth cylindrical functions are dense in energy in these kinds of functional spaces defined over any weighted Banach space.
Source: Monatshefte für Mathematik
Author: Enrico Pasqualetto
Institution: University of Jyväskylä
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4415277694