Happy fractals and some aspects of analysis on metric spaces
Stephen Semmes
Abstract
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.
Create a lesson
Related papers
Schatten--Lorentz properties of commutators with matrix weights
Tuomas Hytönen, Xingyan Quan
Reverse Hölder Class and Two-Parameter Good-λ Inequality over Hausdorff Content
Long Huang, Yangzhi Zhang, Ciqiang Zhuo
Translational self-affine tiles in Rn
Li-Xiang An, Ting-Ting He
Lp-weighted cone restriction estimates
Xiangyu Wang
Two-weight T1 theorem for fractional Riesz transforms: one measure supported on a C1,Dini curve
Ji Li, Chun-Yen Shen, Eric Sawyer et al.
On Mattila's intersection problem in the plane: sharp dimension and positive measure of rotated difference sets
Thang Pham, Chun-Yen Shen, Dung The Tran