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A pointwise characterization of functions of bounded variation on metric spaces

Abstract

We give a new characterization of the space of functions of bounded variation in terms of a pointwise inequality connected to the maximal function of a measure. The characterization is new even in Euclidean spaces and it holds also in general metric spaces.

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Acknowledgments

The authors wish to thank Juha Kinnunen for helpful discussions and suggestions. Part of this research was conducted during the visit of the second author to Forschungsinstitut für Mathematik of ETH Zürich, and she wishes to thank the institute for the kind hospitality. The second author was supported by the Academy of Finland, grant no. 135561.

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Correspondence to Heli Tuominen.

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Communicated by Prof. Salvatore Rionero.

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Lahti, P., Tuominen, H. A pointwise characterization of functions of bounded variation on metric spaces. Ricerche mat. 63, 47–57 (2014). https://doi.org/10.1007/s11587-013-0161-9

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Keywords

  • Functions of bounded variation
  • Metric measure space
  • Pointwise characterization
  • Doubling measure

Mathematics Subject Classification (2000)

  • 46E35
  • 26B30
  • 28A12