Classification of anisotropic Triebel-Lizorkin spaces

2022/11/09 by Koppensteiner, Sarah, van Velthoven, Jordy Timo, Voigtlaender, Felix
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2211.04936

Abstract

This paper provides a classification theorem for expansive matrices A ∈ GL(d, ℝ) generating the same anisotropic homogeneous Triebel-Lizorkin space F^α_{p, q}(A) for α∈ ℝ and p,q ∈ (0,∞]. It is shown that F^α_{p, q}(A) = F^α_{p, q}(B) if and only if the homogeneous quasi-norms ρ_A, ρ_B associated to the matrices A, B are equivalent, except for the case F⁰_{p, 2} = L^p with p ∈ (1,∞). The obtained results complement and extend the classification of anisotropic Hardy spaces H^p(A) = F⁰_p,2(A), p ∈ (0,1], in [Mem. Am. Math. Soc. 781, 122 p. (2003)].

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