A1 Journal article (refereed)
Traces of weighted function spaces : Dyadic norms and Whitney extensions (2017)
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
JYU authors or editors
Publication details
All authors or editors: Koskela, Pekka; Soto, Tomás; Wang, Zhuang
Journal or series: Science China Mathematics
ISSN: 1674-7283
eISSN: 1869-1862
Publication year: 2017
Volume: 60
Issue number: 11
Pages range: 1981-2010
Publisher: Springer
Publication country: China
Publication language: English
DOI: https://doi.org/10.1007/s11425-017-9148-6
Publication open access: Other way freely accessible online
Publication channel open access:
Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/62972
Web address where publication is available: https://arxiv.org/abs/1708.04902
Abstract
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.
Keywords: function analysis; function spaces; applied mathematics
Free keywords: trace theorems; weighted Sobolev spaces; Besov spaces; Triebel-Lizorkin spaces
Contributing organizations
Related projects
- Centre of Excellence in Analysis and Dynamics Research
- Koskela, Pekka
- Academy of Finland
Ministry reporting: Yes
Reporting Year: 2017
JUFO rating: 1