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An integral type characterization of constant functions on metric-measure spaces

Ranjbar Motlagh, A ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1016/j.jmaa.2011.06.020
  3. Publisher: 2012
  4. Abstract:
  5. The main purpose of this article is to generalize a characterization of constant functions to the context of metric-measure spaces. In fact, we approximate a measurable function, in terms of a certain integrability condition, by Lipschitz functions. Then, similar to Brezis (2002) [2], we establish a necessary and sufficient condition in order that any measurable function which satisfies an integrability condition to be constant a.e. Also, we provide a different proof for the main result of Pietruska-Pałuba (2004) [7] in the setting of Dirichlet forms
  6. Keywords:
  7. Doubling condition ; Heat kernel ; Metric-measure spaces
  8. Source: Journal of Mathematical Analysis and Applications ; Volume 385, Issue 1 , January , 2012 , Pages 194-201 ; 0022247X (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0022247X11005683