The reconstruction theorem in Besov spaces
File(s)
Accepted version
Author(s)
Hairer, Martin
Labbe, Cyril
Type
Journal Article
Abstract
The theory of regularity structures [9] sets up an abstract framework of modelled distributions generalising the usual Hölder functions and allowing one to give a meaning to several ill-posed stochastic PDEs. A key result in that theory is the so-called reconstruction theorem: it defines a continuous linear operator that maps spaces of modelled distributions into the usual space of distributions. In the present paper, we extend the scope of this theorem to analogues to the whole class of Besov spaces Bp,qγ with non-integer regularity indices. We then show that these spaces behave very much like their classical counterparts by obtaining the corresponding embedding theorems and Schauder-type estimates.
Date Issued
2017-07-18
Date Acceptance
2017-07-03
Citation
Journal of Functional Analysis, 2017, 273 (8), pp.2578-2618
ISSN
0022-1236
Publisher
Elsevier
Start Page
2578
End Page
2618
Journal / Book Title
Journal of Functional Analysis
Volume
273
Issue
8
Copyright Statement
© 2017, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Subjects
Science & Technology
Physical Sciences
Mathematics
Regularity structures
Besov spaces
Embedding theorems
Schauder estimates
REGULARITY STRUCTURES
Publication Status
Published