Classification of anisotropic Triebel-Lizorkin spaces

Journal article (2023)

Authors

Sarah Koppensteiner University of Vienna
J.T. van Velthoven Analysis - EEMCS
Felix Voigtlaender Katholische Universität Eichstätt - Ingolstadt
Research Group
Analysis (EEMCS) (TU Delft)
Copyright: © 2023 Sarah Koppensteiner, J.T. van Velthoven, Felix Voigtlaender
DOI: https://doi.org/10.1007/s00208-023-02690-y
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Published Date

2023

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

Abstract

This paper provides a characterization of expansive matrices A∈ GL (d, R) generating the same anisotropic homogeneous Triebel–Lizorkin space F˙p,qα(A) for α∈ R and p, q∈ (0 , ∞] . It is shown that F˙p,qα(A)=F˙p,qα(B) if and only if the homogeneous quasi-norms ρA, ρB associated to the matrices A, B are equivalent, except for the case F˙p,20=Lp with p∈ (1 , ∞) . The obtained results complement and extend the classification of anisotropic Hardy spaces Hp(A)=F˙p,20(A) , p∈ (0 , 1] , in Bownik (Mem Am Math Soc 164(781):vi+122, 2003).