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An extension-restriction theorem for weighted Besov spaces

Part of: Harmonic analysis in several variables Special classes of linear operators Linear function spaces and their duals

Published online by Cambridge University Press:  26 August 2025

Dalian Jin ,
Liguang Liu  and
Suqing Wu
Dalian Jin
Affiliation:
School of Mathematics, Renmin University of China , Beijing 100872, People’s Republic of China e-mail: jindalian@ruc.edu.cn liuliguang@ruc.edu.cn
Liguang Liu
Affiliation:
School of Mathematics, Renmin University of China , Beijing 100872, People’s Republic of China e-mail: jindalian@ruc.edu.cn liuliguang@ruc.edu.cn
Suqing Wu*
Affiliation:
School of Science, Dalian Maritime University , Dalian 116024, People’s Republic of China
*
e-mail: wusq@dlmu.edu.cn
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Abstract

In this article, the authors establish an extension-restriction theorem between homogeneous weighted Besov spaces and weighted mixed-Riesz potential spaces. This general frame covers both the classical Besov spaces and their logarithmic analogs.

Keywords

Besov spacesmixed-Riesz potential spacesweightextensionrestriction

MSC classification

Primary: 46E30: Spaces of measurable functions ($L^p$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 42B35: Function spaces arising in harmonic analysis 47B38: Operators on function spaces (general)

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Type
Article
Information
Canadian Journal of Mathematics , First View , pp. 1 - 48
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

L. Liu was supported by the National Natural Science Foundation of China (Grant Nos. 12371102 and 12271021). S. Wu was supported by the National Natural Science Foundation of China (Grant No. 12201098) and the Fundamental Research Funds for the Central Universities (Grant No. 3132024199).

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