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

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

Koppensteiner, Sarah (University of Vienna)
van Velthoven, J.T. (TU Delft Analysis)
Voigtlaender, Felix (Katholische Universität Eichstätt - Ingolstadt)

2023

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. 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.

Anisotropic Triebel–Lizorkin spaces
Anisotropic wavelet systems
Coorbit molecules
Frames
Maximal functions
One-parameter groups
Riesz sequences

http://resolver.tudelft.nl/uuid:319a48a8-bf34-48fd-bd4d-94ad104c7e24

https://doi.org/10.1007/s00605-023-01827-0

0026-9255

Monatshefte für Mathematik, 201 (2), 375-429

Institutional Repository

journal article

© 2023 Sarah Koppensteiner, J.T. van Velthoven, Felix Voigtlaender