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

Abstract

Continuing previous work, this paper provides maximal characterizations of anisotropic Triebel-Lizorkin spaces ${\dot{\mathbf{F}}}_{p,q}^{\alpha }$ 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 ${\dot{\mathbf{B}}}_{\infty ,\infty }^{\alpha }={\dot{\mathbf{F}}}_{\infty ,\infty }^{\alpha }$ is obtained. As a consequence, it is shown that there exist dual molecular frames and Riesz sequences in ${\dot{\mathbf{F}}}_{\infty ,q}^{\alpha }$.