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Balls as Subspaces of Homogeneous Type: On a Construction due to R. Macías and C. Segovia

  • Hugo Aimar
Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Summary

In this chapter we give an equivalent point of view for quasi-metric structures on a set X in terms of families of neighborhoods of the diagonal in X×X. We use this approach and the iterative process introduced by R. Macías and C. Segovia in ‘A well behaved quasi-distance for spaces of homogeneous type' (Trabajos de Matemática, IAM, 32, 1981, 1-18) in order to show that the balls in the new quasi-distance have a specific regularity at the boundary.

Keywords

Homogeneous Type Euclidean Ball Regularization Procedure Family Versus Generalize Dilation 
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References

  1. 1.
    A. P. Calderón and A. Torchinsky: Parabolic maximal functions associated with a distribution, Advances in Math., 16 (1975), 1–64.CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    R. A. Macías and C. A. Segovia: A well behaved quasi-distance for spaces of homogeneous type, Trabajos de Matemática, IAM, 32 (1981), 1–18.Google Scholar

Copyright information

© Birkhäuser Boston 2010

Authors and Affiliations

  1. 1.Instituto de Matemática Aplicada del LitoralCONICET and Universidad Nacional del LitoralSanta FeArgentina

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