Singular Integrals on Self-similar Subsets of Metric Groups

Part of the Trends in Mathematics book series (TM)


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.


Heisenberg Group Hausdorff Dimension Singular Integral Operator Carnot Group Riesz Kernel 
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P.M and V.C were supported by the Academy of Finland.


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Illinois-Urbana ChampaignUrbanaUSA
  2. 2.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland

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