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

Abstract

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