Poincaré inequality and Hajłasz–Sobolev spaces on nested fractals

Volume 218 / 2013

Katarzyna Pietruska-Pałuba, Andrzej Stós Studia Mathematica 218 (2013), 1-26 MSC: Primary 46E35; Secondary 31E05, 28A80. DOI: 10.4064/sm218-1-1

Abstract

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.

Authors

  • Katarzyna Pietruska-PałubaInstitute of Mathematics
    University of Warsaw
    Banacha 2
    02-097 Warszawa, Poland
    e-mail
  • Andrzej StósClermont Université
    Université Blaise Pascal
    Laboratoire de Mathématiques
    CNRS UMR 6620, BP 80026
    63171 Aubière, France
    e-mail

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