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

Sarah Koppensteiner; Jordy Timo van Velthoven; Felix Voigtlaender

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arXiv · 2104.14361

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

Sarah Koppensteiner·Jordy Timo van Velthoven·Felix Voigtlaender

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Abstract

This paper provides maximal function characterizations of anisotropic Triebel-Lizorkin spaces associated to general expansive matrices for the full range of parameters $p \in (0,\infty)$, $q \in (0,\infty]$ and $\alpha \in \mathbb{R}$. 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. As an application, the existence of dual molecular frames and Riesz sequences is obtained; the wavelet systems are generated 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 mild decay, moment, and smoothness conditions.

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Sarah Koppensteiner, Jordy Timo van Velthoven, Felix Voigtlaender. 2021-04-29. Anisotropic Triebel-Lizorkin spaces and wavelet coefficient decay over one-parameter dilation groups, I. https://arxiv.org/abs/2104.14361

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