Traces of weighted function spaces : Dyadic norms and Whitney extensions
Koskela, P., Soto, T., & Wang, Z. (2017). Traces of weighted function spaces : Dyadic norms and Whitney extensions. Science China Mathematics, 60(11), 1981-2010. https://doi.org/10.1007/s11425-017-9148-6
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© Science China Press and Springer-Verlag Berlin Heidelberg 2017.
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.
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Centre of Excellence, AoFAdditional information about funding
This work was supported by the Academy of Finland via the Centre of Excellence in Analysis and Dynamics Research (Grant No. 307333).License
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