The reconstruction theorem in Besov spaces
Hairer, Martin; Labbé, Cyril (2017), The reconstruction theorem in Besov spaces, Journal of Functional Analysis, 273, 8, p. 2578 - 2618. 10.1016/j.jfa.2017.07.002
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1609.04543
Journal nameJournal of Functional Analysis
2578 - 2618
MetadataShow full item record
Warwick Mathematics Institute [WMI]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)The theory of regularity structures sets up an abstract framework of modelled distributions generalising the usual H\"older 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 Bγp,q 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.
Subjects / KeywordsRegularity structures; Besov spaces; Embedding theorems; Schauder estimates
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