Anisotropic Triebel-Lizorkin spaces and wavelet coefficient decay over one-parameter dilation groups, II

Continuing previous work, this paper provides maximal characterizations of anisotropic Triebel-Lizorkin spaces $\dot{\mathbf{F}}^α_{p,q}$ for the endpoint case of $p = \infty$ and the full scale of parameters $α\in \mathbb{R}$ and $q \in (0,\infty]$. In particular, a Peetre-type characterization of the anisotropic Besov space $\dot{\mathbf{B}}^α_{\infty,\infty} = \dot{\mathbf{F}}^α_{\infty,\infty}$ is obtained. As a consequence, it is shown that there exist dual molecular frames and Riesz sequences in $\dot{\mathbf{F}}^α_{\infty,q}$.

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