Modelled distributions of Triebel–Lizorkin type

Hensel S, Rosati T. 2020. Modelled distributions of Triebel–Lizorkin type. Studia Mathematica. 252(3), 251–297.

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Author
Hensel, SebastianIST Austria ; Rosati, Tommaso
Abstract
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.
Publishing Year
Date Published
2020-03-01
Journal Title
Studia Mathematica
Volume
252
Issue
3
Page
251-297
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Hensel S, Rosati T. Modelled distributions of Triebel–Lizorkin type. Studia Mathematica. 2020;252(3):251-297. doi:10.4064/sm180411-11-2
Hensel, S., & Rosati, T. (2020). Modelled distributions of Triebel–Lizorkin type. Studia Mathematica. Institute of Mathematics, Polish Academy of Sciences. https://doi.org/10.4064/sm180411-11-2
Hensel, Sebastian, and Tommaso Rosati. “Modelled Distributions of Triebel–Lizorkin Type.” Studia Mathematica. Institute of Mathematics, Polish Academy of Sciences, 2020. https://doi.org/10.4064/sm180411-11-2.
S. Hensel and T. Rosati, “Modelled distributions of Triebel–Lizorkin type,” Studia Mathematica, vol. 252, no. 3. Institute of Mathematics, Polish Academy of Sciences, pp. 251–297, 2020.
Hensel S, Rosati T. 2020. Modelled distributions of Triebel–Lizorkin type. Studia Mathematica. 252(3), 251–297.
Hensel, Sebastian, and Tommaso Rosati. “Modelled Distributions of Triebel–Lizorkin Type.” Studia Mathematica, vol. 252, no. 3, Institute of Mathematics, Polish Academy of Sciences, 2020, pp. 251–97, doi:10.4064/sm180411-11-2.

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