Happy fractals and some aspects of analysis on metric spaces

Details Happy fractals and some aspects of analysis on metric spaces Happy fractals and some aspects of analysis on metric spaces

2002-11-07

arxiv.org/abs/math/0211136v3

Publicacions Matematiques (Barcelona), Volume 47 (2003), 261--309

Mathematics

Classical Analysis and ODEs

latex-2e, 50 pages. Combined with two other articles, and various additions and adjustments

Scientific paper

By a "happy fractal" we mean a metric space with bounded geometry in the sense of a doubling condition and a lot of paths of finite length, so that any pair of points can be connected by a path whose length is less than or equal to a constant times the distance between the two points. In these notes we consider some examples, related notions, and other aspects of analysis on metric spaces. This includes Lipschitz functions of some positive order and the special class of functions known as "atoms" which are related to singular integral operators.

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