Morneau-Guérin, Frédéric 
ORCID: https://orcid.org/0000-0001-7610-4648
(2026).
Exact discrete reductions for nexted Hardy inequalities. Matematichki Bilten, 50 (1), 17-39.
|
PDF
- note_nested_averages_bilten_R1.pdf
Contenu du fichier : Manuscrit accepté (révisé après évaluation) Accès restreint jusqu'à fin- 1 juillet 2027. |
|
| Catégorie de document : | Articles de revues |
|---|---|
| Évaluation par un comité de lecture : | Oui |
| Étape de publication : | Publié |
| Résumé : | Bouthat and Parisé (arXiv:2606.24044) characterized weighted Hardy inequalities for averages over nested sets and asked three questions, on function spaces beyond L^p, on triangular kernel operators, and on sums of integrals over different measure spaces. We answer all three by the same reduction, which shows that the measure-theoretic inequality is equivalent, with the same optimal constant, to a discrete one. This settles the multi-space question and completes the exponent picture for nested averages, the case 0<q<p being resolved for all p in [1,infinity). For a Banach function space over the whole space, the right discrete object is a quotient functional on sequences, which cannot in general be recovered from the associate norms on the pieces. For direct sums of spaces over the pieces, the reduction leads exactly to these associate norms. Triangular kernels reduce, through an exact dual formula, to their column functionals. These are determined by the local norms alone when the kernel is block-factorized, and Oinarov-type criteria then hold for 1<p < q< infinity and 1<q<p< infinity. |
| Adresse de la version officielle : | https://bilten.smm.org.mk/index.php/bilten/article... |
| Déposant: | Morneau-Guérin, Frédéric |
| Responsable : | Frédéric Morneau-Guérin |
| Dépôt : | 05 nov. 2026 14:37 |
| Dernière modification : | 05 nov. 2026 14:37 |
|
RÉVISER |
