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Singular Integrals on Self-similar Subsets of Metric Groups

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Further Developments in Fractals and Related Fields

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Abstract

In this chapter we study singular integrals on small (i.e., measure zero and lower than full dimensional) subsets of metric groups. The main examples of the groups we have in mind are Euclidean spaces and Heisenberg groups. We shall pay particular attention to the behaviour of singular integral operators on self-similar subsets.

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Acknowledgements

P.M and V.C were supported by the Academy of Finland.

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Authors and Affiliations

  1. Department of Mathematics, University of Illinois-Urbana Champaign, 1409 W. Green St, IL, 61801, Urbana, USA

    Vasilis Chousionis

  2. Department of Mathematics and Statistics, University of Helsinki, Helsinki, 68, FI-00014, Finland

    Pertti Mattila

Authors
  1. Vasilis Chousionis
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  2. Pertti Mattila
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Correspondence to Vasilis Chousionis .

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Editors and Affiliations

  1. , LAGA, Université Paris 13, avenue J.B. Clément 99, Villetaneuse, 93430, France

    Julien Barral

  2. , Laboratoire d'Analyse et de Mathématique, Université Paris-Est Créteil - Val de Ma, Avenue du Général de Gaulle 61, Créteil Cedex, 94010, France

    Stéphane Seuret

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Chousionis, V., Mattila, P. (2013). Singular Integrals on Self-similar Subsets of Metric Groups. In: Barral, J., Seuret, S. (eds) Further Developments in Fractals and Related Fields. Trends in Mathematics. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-8400-6_4

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