---
_id: '9196'
abstract:
- lang: eng
  text: In order to provide a local description of a regular function in a small neighbourhood
    of a point x, it is sufficient by Taylor’s theorem to know the value of the function
    as well as all of its derivatives up to the required order at the point x itself.
    In other words, one could say that a regular function is locally modelled by the
    set of polynomials. The theory of regularity structures due to Hairer generalizes
    this observation and provides an abstract setup, which in the application to singular
    SPDE extends the set of polynomials by functionals constructed from, e.g., white
    noise. In this context, the notion of Taylor polynomials is lifted to the notion
    of so-called modelled distributions. The celebrated reconstruction theorem, which
    in turn was inspired by Gubinelli’s \textit {sewing lemma}, is of paramount importance
    for the theory. It enables one to reconstruct a modelled distribution as a true
    distribution on Rd which is locally approximated by this extended set of models
    or “monomials”. In the original work of Hairer, the error is measured by means
    of Hölder norms. This was then generalized to the whole scale of Besov spaces
    by Hairer and Labbé. It is the aim of this work to adapt the analytic part of
    the theory of regularity structures to the scale of Triebel–Lizorkin spaces.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Sebastian
  full_name: Hensel, Sebastian
  id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
  last_name: Hensel
  orcid: 0000-0001-7252-8072
- first_name: Tommaso
  full_name: Rosati, Tommaso
  last_name: Rosati
citation:
  ama: Hensel S, Rosati T. Modelled distributions of Triebel–Lizorkin type. <i>Studia
    Mathematica</i>. 2020;252(3):251-297. doi:<a href="https://doi.org/10.4064/sm180411-11-2">10.4064/sm180411-11-2</a>
  apa: Hensel, S., &#38; Rosati, T. (2020). Modelled distributions of Triebel–Lizorkin
    type. <i>Studia Mathematica</i>. Instytut Matematyczny. <a href="https://doi.org/10.4064/sm180411-11-2">https://doi.org/10.4064/sm180411-11-2</a>
  chicago: Hensel, Sebastian, and Tommaso Rosati. “Modelled Distributions of Triebel–Lizorkin
    Type.” <i>Studia Mathematica</i>. Instytut Matematyczny, 2020. <a href="https://doi.org/10.4064/sm180411-11-2">https://doi.org/10.4064/sm180411-11-2</a>.
  ieee: S. Hensel and T. Rosati, “Modelled distributions of Triebel–Lizorkin type,”
    <i>Studia Mathematica</i>, vol. 252, no. 3. Instytut Matematyczny, pp. 251–297,
    2020.
  ista: Hensel S, Rosati T. 2020. Modelled distributions of Triebel–Lizorkin type.
    Studia Mathematica. 252(3), 251–297.
  mla: Hensel, Sebastian, and Tommaso Rosati. “Modelled Distributions of Triebel–Lizorkin
    Type.” <i>Studia Mathematica</i>, vol. 252, no. 3, Instytut Matematyczny, 2020,
    pp. 251–97, doi:<a href="https://doi.org/10.4064/sm180411-11-2">10.4064/sm180411-11-2</a>.
  short: S. Hensel, T. Rosati, Studia Mathematica 252 (2020) 251–297.
date_created: 2021-02-25T08:55:03Z
date_published: 2020-03-01T00:00:00Z
date_updated: 2023-10-17T09:15:53Z
day: '01'
department:
- _id: JuFi
- _id: GradSch
doi: 10.4064/sm180411-11-2
external_id:
  arxiv:
  - '1709.05202'
  isi:
  - '000558100500002'
intvolume: '       252'
isi: 1
issue: '3'
keyword:
- General Mathematics
language:
- iso: eng
month: '03'
oa_version: Preprint
page: 251-297
publication: Studia Mathematica
publication_identifier:
  eissn:
  - 1730-6337
  issn:
  - 0039-3223
publication_status: published
publisher: Instytut Matematyczny
quality_controlled: '1'
scopus_import: '1'
status: public
title: Modelled distributions of Triebel–Lizorkin type
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 252
year: '2020'
...