Stephen Semmes
Published 2002-11-07, updated 2003-03-20Version 3
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.
Comments: latex-2e, 50 pages. Combined with two other articles, and various additions and adjustments
Journal: Publicacions Matematiques (Barcelona), Volume 47 (2003), 261--309
A note on weak convergence of singular integrals in metric spaces
Fractional Poincaré and localized Hardy inequalities on metric spaces
Even singular integral operators that are well behaved on a purely unrectifiable set
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