Democracy of quasi-greedy bases in -Banach spaces with applications to the efficiency of the Thresholding Greedy Algorithm in the Hardy spaces
We use new methods, specific for non-locally convex quasi-Banach spaces, to investigate when the quasi-greedy bases of a $p$ -Banach space for $0< p<1$ are democratic. The novel techniques we obtain permit to show in particular that all quasi-greedy bases of the Hardy space $H_p({\mathbb {D}})...
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| Veröffentlicht in: | Proceedings of the Royal Society of Edinburgh. Section A. Mathematics Jg. 154; H. 3; S. 906 - 928 |
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| Hauptverfasser: | , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Cambridge
Cambridge University Press
01.06.2024
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| Schlagworte: | |
| ISSN: | 0308-2105, 1473-7124 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We use new methods, specific for non-locally convex quasi-Banach spaces, to investigate when the quasi-greedy bases of a
$p$
-Banach space for
$0< p<1$
are democratic. The novel techniques we obtain permit to show in particular that all quasi-greedy bases of the Hardy space
$H_p({\mathbb {D}})$
for
$0< p<1$
are democratic while, in contrast, no quasi-greedy basis of
$H_p({\mathbb {D}}^d)$
for
$d\ge 2$
is, solving thus a problem that was raised in [7]. Applications of our results to other spaces of interest both in functional analysis and approximation theory are also provided. |
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| Bibliographie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0308-2105 1473-7124 |
| DOI: | 10.1017/prm.2023.42 |