TY - JOUR
T1 - Classification of anisotropic Triebel-Lizorkin spaces
AU - Koppensteiner, Sarah
AU - van Velthoven, Jordy Timo
AU - Voigtlaender, Felix
PY - 2023
Y1 - 2023
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=85166616454&partnerID=8YFLogxK
U2 - 10.1007/s00208-023-02690-y
DO - 10.1007/s00208-023-02690-y
M3 - Article
AN - SCOPUS:85166616454
SN - 0025-5831
VL - 389
SP - 1883
EP - 1923
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 2
ER -