Science China Mathematics

, Volume 60, Issue 11, pp 1981–2010 | Cite as

Traces of weighted function spaces: Dyadic norms and Whitney extensions

  • Pekka Koskela
  • Tomás Soto
  • Zhuang Wang


The trace spaces of Sobolev spaces and related fractional smoothness spaces have been an active area of research since the work of Nikolskii, Aronszajn, Slobodetskii, Babich and Gagliardo among others in the 1950’s. In this paper, we review the literature concerning such results for a variety of weighted smoothness spaces. For this purpose, we present a characterization of the trace spaces (of fractional order of smoothness), based on integral averages on dyadic cubes, which is well-adapted to extending functions using the Whitney extension operator.


trace theorems weighted Sobolev spaces Besov spaces Triebel-Lizorkin spaces 


46E35 42B35 


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This work was supported by the Academy of Finland via the Centre of Excellence in Analysis and Dynamics Research (Grant No. 307333).


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Copyright information

© Science China Press and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of JyväskyläJyväskyläFinland

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