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