JournalsjfgVol. 5, No. 2pp. 143–164

Sobolev algebra counterexamples

  • Thierry Coulhon

    Université de Cergy-Pontoise, France
  • Luke G. Rogers

    University of Connecticut, Storrs, USA
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In the Euclidean setting the Sobolev spaces Wα,pLW^{\alpha,p}\cap L^\infty are algebras for the pointwise product when α>0\alpha > 0 and p(1,)p\in(1,\infty). This property has recently been extended to a variety of geometric settings. We produce a class of fractal examples where it fails for a wide range of the indices α,p\alpha,p.

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Thierry Coulhon, Luke G. Rogers, Sobolev algebra counterexamples. J. Fractal Geom. 5 (2018), no. 2, pp. 143–164

DOI 10.4171/JFG/59