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.
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References
A. P. Calderón and A. Torchinsky: Parabolic maximal functions associated with a distribution, Advances in Math., 16 (1975), 1–64.
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.
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Aimar, H. (2010). Balls as Subspaces of Homogeneous Type: On a Construction due to R. Macías and C. Segovia. In: Cabrelli, C., Torrea, J. (eds) Recent Developments in Real and Harmonic Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4588-5_2
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DOI: https://doi.org/10.1007/978-0-8176-4588-5_2
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