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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Characterization of nonlinear Besov spaces


Authors: Chong Liu, David J. Prömel and Josef Teichmann
Journal: Trans. Amer. Math. Soc. 373 (2020), 529-550
MSC (2010): Primary 30H25, 46E35, 54C35
DOI: https://doi.org/10.1090/tran/7968
Published electronically: October 1, 2019
MathSciNet review: 4042884
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Abstract: The canonical generalizations of two classical norms on Besov spaces are shown to be equivalent even in the case of nonlinear Besov spaces, that is, function spaces consisting of functions taking values in a metric space and equipped with some Besov-type topology. The proofs are based on atomic decomposition techniques and metric embeddings. Additionally, we provide embedding results showing how nonlinear Besov spaces embed in nonlinear $ p$-variation spaces, and vice versa. We emphasize that we assume neither the unconditional martingale difference property of the involved spaces nor their separability.


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Additional Information

Chong Liu
Affiliation: Eidgenössische Technische Hochschule Zürich, Zürich, Switzerland
Email: chong.liu@math.ethz.ch

David J. Prömel
Affiliation: University of Oxford, Oxford, United Kingdom
Email: proemel@maths.ox.ac.uk

Josef Teichmann
Affiliation: Eidgenössische Technische Hochschule Zürich, Zürich, Switzerland
Email: josef.teichmann@math.ethz.ch

DOI: https://doi.org/10.1090/tran/7968
Keywords: Atomic decomposition, Besov space, embedding theorem, metric space, $p$-variation, fractional Sobolev space.
Received by editor(s): March 6, 2019
Received by editor(s) in revised form: June 29, 2019
Published electronically: October 1, 2019
Additional Notes: The first and third authors gratefully acknowledge support from the ETH Foundation.
The third author gratefully acknowledges support from SNF project 163425.
Article copyright: © Copyright 2019 American Mathematical Society