Traces to Closed Subsets:Criteria, Applications

  • Alexander BrudnyiEmail author
  • Yuri Brudnyi
Part of the Monographs in Mathematics book series (MMA, volume 103)


Section 9.1 presents the Yu. Brudnyi and Shvartsman criteria characterizing the trace spaces for Lipschitz functions of higher order and those for the associated jet spaces. Their proofs widely exploit the concepts and methods of Local Approximation Theory. In particular, the key tools are the Yu. Brudnyi inequality relating local approximation to the corresponding di_erence characteristic, see Volume I, Theorem 2.37, and a Whitney type extension construction with Taylor polynomials replaced by polynomials of the best local approximation.


Closed Subset Extension Operator Trace Space Uniform Domain Campanato Space 
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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of Mathematics & StatisticsUniversity of CalgaryCalgaryCanada
  2. 2.Mathematics DepartmentTechnion - Israel Institute of TechnologyHaifaIsrael

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