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Integrability of Green potentials in fractal domains

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Arkiv för Matematik

Abstract

We proveL q-inequalities for the gradient of the Green potential (Gf) in bounded, connected NTA-domains inR n,n≥2. These domains may have a highly non-rectifiable boundary and in the plane the set of all bounded simply connected NTA-domains coincides with the set of all quasidiscs. We get a restriction on the exponentq for which our inequalities are valid in terms of the validity of a reverse Hölder inequality for the Green function close to the boundary.

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Author notes

  1. Kaj Nyström

    Present address: Department of Mathematics, The University of Chicago, 5734 University Avenue, 60637, Chicago, IL, U.S.A.

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  1. Department of Mathematics, University of Umeå, S-90187, Umeå, Sweden

    Kaj Nyström

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  1. Kaj Nyström
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Nyström, K. Integrability of Green potentials in fractal domains. Ark. Mat. 34, 335–381 (1996). https://doi.org/10.1007/BF02559551

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  • DOI: https://doi.org/10.1007/BF02559551

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