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

Kurzfassung/Abstract

This paper provides maximal function characterizations of anisotropic Triebel-Lizorkin spaces associated to general expansive matrices for the full range of parameters p∈(0,∞), q∈(0,∞] and α∈R. The equivalent norm is defined in terms of the decay of wavelet coefficients, quantified by a Peetre-type space over a one-parameter dilation group. For the Banach space regime p,q≥1, we use this characterization to prove the existence of frames and Riesz sequences of dual molecules for the Triebel-Lizorkin spaces; the atoms are obtained by translations and anisotropic dilations of a single function, where neither the translation nor dilation parameters are required to belong to a discrete subgroup. Explicit criteria for molecules are given in terms of smoothness, decay and moment conditions.