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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

Traces of $ C^k$ functions on weak Markov subsets of $ \mathbb{R}^n$


Authors: A. Brudnyĭ and Yu. Brudnyĭ
Translated by: the authors
Original publication: Algebra i Analiz, tom 23 (2011), nomer 1.
Journal: St. Petersburg Math. J. 23 (2012), 39-56
MSC (2010): Primary 26B35
Published electronically: November 7, 2011
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Abstract: A wide class of closed subsets of $ \mathbb{R}^n$ is introduced; these subsets admit constructive $ C^{k,\omega}$ extensions with good bounds for the corresponding extension constants.


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Additional Information

A. Brudnyĭ
Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary, Canada
Email: albru@math.ucalgary.ca

Yu. Brudnyĭ
Affiliation: Department of Mathematics, Technion, Haifa, Israel
Email: ybrudnyi@math.technion.ac.il

DOI: http://dx.doi.org/10.1090/S1061-0022-2011-01185-9
PII: S 1061-0022(2011)01185-9
Keywords: Weak Markov sets, linear $C^{k, \omega}$ extension, finiteness constants, depth of finite order
Received by editor(s): August 20, 2010
Published electronically: November 7, 2011
Additional Notes: Research of the first author was supported in part by NSERC
Dedicated: In memory of Mikhail Shlemovich Birman
Article copyright: © Copyright 2011 American Mathematical Society