Metric Sobolev spaces

Koskela, Pekka

  • Nonlinear Analysis, Function Spaces and Applications, Publisher: Czech Academy of Sciences, Mathematical Institute(Praha), page 133-147

Abstract

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We describe an approach to establish a theory of metric Sobolev spaces based on Lipschitz functions and their pointwise Lipschitz constants and the Poincaré inequality.

How to cite

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Koskela, Pekka. "Metric Sobolev spaces." Nonlinear Analysis, Function Spaces and Applications. Praha: Czech Academy of Sciences, Mathematical Institute, 2003. 133-147. <http://eudml.org/doc/220171>.

@inProceedings{Koskela2003,
abstract = {We describe an approach to establish a theory of metric Sobolev spaces based on Lipschitz functions and their pointwise Lipschitz constants and the Poincaré inequality.},
author = {Koskela, Pekka},
booktitle = {Nonlinear Analysis, Function Spaces and Applications},
keywords = {Lipschitz function; Poicaré inequality; upper gradient; Sobolev space},
location = {Praha},
pages = {133-147},
publisher = {Czech Academy of Sciences, Mathematical Institute},
title = {Metric Sobolev spaces},
url = {http://eudml.org/doc/220171},
year = {2003},
}

TY - CLSWK
AU - Koskela, Pekka
TI - Metric Sobolev spaces
T2 - Nonlinear Analysis, Function Spaces and Applications
PY - 2003
CY - Praha
PB - Czech Academy of Sciences, Mathematical Institute
SP - 133
EP - 147
AB - We describe an approach to establish a theory of metric Sobolev spaces based on Lipschitz functions and their pointwise Lipschitz constants and the Poincaré inequality.
KW - Lipschitz function; Poicaré inequality; upper gradient; Sobolev space
UR - http://eudml.org/doc/220171
ER -

References

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  10. Koskela P., Onninen J., Sharp inequalities via truncation, J. Math. Anal. Appl. 278 (2003), 324–334. Zbl1019.26003MR1974010
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  12. Lu G., Wheeden R. L., High order representation formulas and embedding theorems on stratified groups and generalizations, Studia Math. 142 (2000), 101–133. Zbl 0974.46039, MR 2001k:46055. Zbl0974.46039MR1792599
  13. Malý J., Pick L., The sharp Riesz potential estimates in metric spaces, Indiana Univ. Math. J. 51 (2002), 251–268. Zbl pre01780940, MR 2003d:46045. Zbl1038.46027MR1909289
  14. Rissanen J., Wavelets on self-similar sets and the structure of the spaces M 1 , p ( E , μ ) , Ann. Acad. Sci. Fenn. Math. Diss. 125 (2002). Zbl 0993.42016, MR 2002k:42081. MR1880640
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