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Geometric analysis on Cantor sets and trees by Anders Björn; Jana Björn; James T. Gill; Nageswari Shanmugalingam is a Mathematics article available to read on EtoBox.

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## Abstract Using uniformization, Cantor type sets can be regarded as boundaries of rooted trees. In this setting, we show that the trace of a first-order Sobolev space on the boundary of a regular rooted tree is exactly a Besov space with an explicit smoothness exponent. Further, we study quasisymmetries between the boundaries of two trees, and show that they have rough quasiisometric extensions to the trees. Conversely, we show that every rough quasiisometry between two trees extends as a quasisymmetry between their boundaries. In both directions we give sharp estimates for the involved constants. We use this to obtain quasisymmetric invariance of certain Besov spaces of functions on Cantor type sets.

Who reads Geometric analysis on Cantor sets and trees?

Author

Anders Björn; Jana Björn; James T. Gill; Nageswari Shanmugalingam

Publisher

Walter de Gruyter GmbH

Published

2014

Language

EN

Field

Mathematics (Physical Sciences)