Anisotropic Triebel–Lizorkin spaces and wavelet coefficient decay over one-parameter dilation groups, I
| Autor: | Sarah Koppensteiner, Jordy Timo van Velthoven, Felix Voigtlaender |
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| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: |
Mathematics - Functional Analysis
One-parameter groups Frames Anisotropic Triebel–Lizorkin spaces Anisotropic wavelet systems Mathematics - Classical Analysis and ODEs General Mathematics Riesz sequences Classical Analysis and ODEs (math.CA) FOS: Mathematics Maximal functions Coorbit molecules Functional Analysis (math.FA) |
| Zdroj: | Monatshefte für Mathematik, 201(2) |
| ISSN: | 0026-9255 |
| Popis: | This paper provides maximal function characterizations of anisotropic Triebel–Lizorkin spaces associated to general expansive matrices for the full range of parameters $$p \in (0,\infty )$$ p ∈ ( 0 , ∞ ) , $$q \in (0,\infty ]$$ q ∈ ( 0 , ∞ ] and $$\alpha \in {\mathbb {R}}$$ 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. |
| Databáze: | OpenAIRE |
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