We present a classification result for homogeneous anisotropic Triebel-Lizorkin spaces F^\alpha_{p,q}(A) associated to expansive dilation matrices A. More precisely, it holds that F^\alpha_{p,q}(A) = F^\alpha_{p,q}(B) if and only if the quasi-norms induced by A and B are equivalent (except when F^0_{p,2}=L^p where equivalence of the quasi-norms is not necessary). Familiarity with anisotropic function spaces is not required for this talk. We will introduce the necessary notions about expansive matrices, their quasi-norms and anisotropic wavelets.
This is joint work with Jordy van Velthoven and Felix Voigtlaender.
https://univienna.zoom.us/j/66031419470?pwd=bXd3V0xEMWM0MTQwS09nWStEV0NnUT09