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

Ministry reporting: Yes

Reporting Year: 2017

JUFO rating: 1