Geodesic
Poincaré inequality and Hajłasz–Sobolev spaces on nested fractals
Katarzyna Pietruska-Pałuba1 ; Andrzej Stós2
1Institute of Mathematics University of Warsaw Banacha 2 02-097 Warszawa, Poland
2Clermont Université Université Blaise Pascal Laboratoire de Mathématiques CNRS UMR 6620, BP 80026 63171 Aubière, France
Studia Mathematica, Tome 218 (2013) no. 1, pp. 1-26
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Given a nondegenerate harmonic structure, we prove a Poincaré-type inequality for functions in the domain of the Dirichlet form on nested fractals. We then study the Hajłasz–Sobolev spaces on nested fractals. In particular, we describe how the “weak”-type gradient on nested fractals relates to the upper gradient defined in the context of general metric spaces.
DOI : 10.4064/sm218-1-1
Keywords: given nondegenerate harmonic structure prove poincar type inequality functions domain dirichlet form nested fractals study haj asz sobolev spaces nested fractals particular describe weak type gradient nested fractals relates upper gradient defined context general metric spaces

Katarzyna Pietruska-Pałuba  1   ; Andrzej Stós  2

1 Institute of Mathematics University of Warsaw Banacha 2 02-097 Warszawa, Poland
2 Clermont Université Université Blaise Pascal Laboratoire de Mathématiques CNRS UMR 6620, BP 80026 63171 Aubière, France 
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 on nested fractals
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Katarzyna Pietruska-Pałuba; Andrzej Stós. Poincaré inequality and Hajłasz–Sobolev spaces
 on nested fractals. Studia Mathematica, Tome 218 (2013) no. 1, pp. 1-26. doi: 10.4064/sm218-1-1

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