Reconstruction theorem in quasinormed spaces

TL;DR

This paper generalizes the Hairer reconstruction theorem to a broader class of function spaces, including Besov and Triebel-Lizorkin spaces with exponents below 1, enhancing the theoretical framework for distribution reconstruction.

Contribution

It extends the reconstruction theorem to new function spaces satisfying translation and scaling, broadening its applicability in analysis.

Findings

Reconstruction theorem now applies to Besov spaces with exponents below 1.

Includes Triebel-Lizorkin spaces in the generalized framework.

Provides theoretical foundation for distribution analysis in broader spaces.

Abstract

We extend the Hairer reconstruction theorem for distributions due to Caravenna and Zambotti (arXiv:2005.09287) to general function spaces satisfying a translation and scaling condition. This includes Besov type spaces with exponents below 1 and Triebel-Lizorkin type spaces.