Abstract Hardy inequalities: The case p=1
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910680988254208 |
|---|---|
| author | Hidalgo, Alejandro Santacruz |
| author_facet | Hidalgo, Alejandro Santacruz |
| contents | Boundedness of an abstract formulation of Hardy operators between Lebesgue spaces over general measure spaces is studied and, when the domain is L^1, shown to be equivalent to the existence of a Hardy inequality on the half line with general Borel measures. This is done by extending the greatest decreasing minorant construction to general measure spaces depending on a totally ordered collection of measurable sets, called an ordered core. A functional description of the greatest decreasing minorant is given, and for a large class of ordered cores, a pointwise description is provided. As an application, characterizations of Hardy inequalities for metric measure spaces are given, we note that the metric measure space is not required to admit a polar decomposition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13335 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Abstract Hardy inequalities: The case p=1 Hidalgo, Alejandro Santacruz Functional Analysis 26D15 (Primary) 26D10, 47G10 (Secondary) Boundedness of an abstract formulation of Hardy operators between Lebesgue spaces over general measure spaces is studied and, when the domain is L^1, shown to be equivalent to the existence of a Hardy inequality on the half line with general Borel measures. This is done by extending the greatest decreasing minorant construction to general measure spaces depending on a totally ordered collection of measurable sets, called an ordered core. A functional description of the greatest decreasing minorant is given, and for a large class of ordered cores, a pointwise description is provided. As an application, characterizations of Hardy inequalities for metric measure spaces are given, we note that the metric measure space is not required to admit a polar decomposition. |
| title | Abstract Hardy inequalities: The case p=1 |
| topic | Functional Analysis 26D15 (Primary) 26D10, 47G10 (Secondary) |
| url | https://arxiv.org/abs/2402.13335 |