Classification of anisotropic Triebel-Lizorkin spaces
Sarah Koppensteiner (University of Vienna)
Jordy Timo van Velthoven (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Felix Voigtlaender (Katholische Universität Eichstätt - Ingolstadt)
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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).
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