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An integral type characterization of lipschitz functions over metric-measure spaces

Ranjbar Motlagh, A ; Sharif University of Technology | 2019

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  1. Type of Document: Article
  2. DOI: 10.1016/j.jmaa.2019.07.019
  3. Publisher: Academic Press Inc , 2019
  4. Abstract:
  5. The main purpose of this article is to generalize a characterization of Lipschitz functions in the context of metric-measure spaces. The results are established in the class of metric-measure spaces which satisfy a strong version of the doubling (Bishop-Gromov regularity) condition. Indeed, we establish a necessary and sufficient condition in order that any measurable function which satisfies an integrability condition to be essentially Lipschitzian. © 2019 Elsevier Inc
  6. Keywords:
  7. Change of variables formula ; Generalized doubling spaces ; Lipschitz functions
  8. Source: Journal of Mathematical Analysis and Applications ; Volume 479, Issue 2 , 2019 , Pages 1708-1714 ; 0022247X (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0022247X19305803