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 $$\dot{\textbf{F}}^{\alpha }_{p,q}$$ F ˙ p , q α for the endpoint case $$p = \infty $$ = ∞ and full scale parameters $$\alpha \in \mathbb {R}$$ ∈ R $$q (0,\infty ]$$ ( 0 ] . In particular, a Peetre-type characterization Besov space $$\dot{\textbf{B}}^{\alpha }_{\infty ,\infty } \dot{\textbf{F}}^{\alpha }$$ B is obtained. As consequence, it shown that there exist dual molecular frames Riesz sequences in ,q}$$