Year: 2026
Type: article
Abstract: We provide new characterizations of Sobolev spaces that are true under some mild conditions. We study modified first order Sobolev spaces on metric measure spaces: $${{\,\mathrm{\textrm{TC}}\,}}$$ TC -Newtonian space, $$\hat{{{\,\mathrm{\textrm{TC}}\,}}}$$ TC ^ -Newtonian space, and Ambrosio–Gigli–Savaré-like space. We prove that if the measure is Borel regular and $$\sigma $$ σ -finite, then the modified $${{\,\mathrm{\textrm{TC}}\,}}$$ TC -Newtonian space is equivalent to the Hajłasz–Sobolev space. Moreover, if additionally the measure is doubling then all modified spaces are equivalent to the Hajłasz–Sobolev space.
Source: Annals of Functional Analysis
Authors: Przemysław Górka, Kacper Kurowski
Institution: Warsaw University of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W4406058748