Article
| Title: | A note on nontrivial acting functions for homogeneous Besov and Triebel-Lizorkin spaces (English) |
| Author: | Moussai, Madani |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 75 |
| Issue: | 4 |
| Year: | 2025 |
| Pages: | 1333-1345 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We prove the acting by composition of nontrivial functions $f \colon \mathbb {R} \to \mathbb {R}$ (i.e., ${T_f \colon g\to f\circ g}$) on homogeneous Besov and Triebel-Lizorkin spaces realized as subspaces of ${\mathcal S}'(\mathbb {R}^n)$ in case $s=n/p<1+1/p$, and $q>1$ (Besov space) and $p>1$ (Triebel-Lizorkin space). These subspaces are dilation invariant and endowed with quasi-seminorms such that $\|g\|=0$ if and only if $g$ is constant. (English) |
| Keyword: | composition operator |
| Keyword: | homogeneous Besov space |
| Keyword: | homogeneous Triebel-Lizorkin space |
| Keyword: | realization |
| MSC: | 46E35 |
| MSC: | 47H30 |
| DOI: | 10.21136/CMJ.2025.0116-25 |
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| Date available: | 2025-12-20T07:50:01Z |
| Last updated: | 2025-12-22 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153246 |
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