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Geometric analysis on Cantor sets and trees
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-9677-8321
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-1238-6751
St Louis University, MO 63103 USA.
University of Cincinnati, OH 45221 USA.
2017 (English)In: Journal für die Reine und Angewandte Mathematik, ISSN 0075-4102, E-ISSN 1435-5345, Vol. 725, 63-114 p.Article in journal (Refereed) Published
Abstract [en]

dUsing 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.

Place, publisher, year, edition, pages
WALTER DE GRUYTER GMBH , 2017. Vol. 725, 63-114 p.
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-136880DOI: 10.1515/crelle-2014-0099ISI: 000397635600003OAI: oai:DiVA.org:liu-136880DiVA: diva2:1092097
Note

Funding Agencies|Swedish Research Council; Swedish Fulbright Commission; Charles Phelps Taft Research Center at the University of Cincinnati; University of Washington; NSF Mathematical Sciences Postdoctoral Research Fellowship [DMS-1004721]; Taft Research Center; Simons Foundation [200474]; NSF [DMS-1200915]

Available from: 2017-04-30 Created: 2017-04-30 Last updated: 2017-04-30

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CiteExportLink to record
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Citation style
  • apa
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