Convolution-type operators in grand Lorentz spaces
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910831865757696 |
|---|---|
| author | Nursultanov, Erlan D. Rafeiro, Humberto Suragan, Durvudkhan |
| author_facet | Nursultanov, Erlan D. Rafeiro, Humberto Suragan, Durvudkhan |
| contents | We introduce and study a novel grand Lorentz space-that we believe is appropriate for critical cases-that lies "between" the Lorentz-Karamata space and the recently defined grand Lorentz space from [1]. We prove both Young's and O'Neil's inequalities in the newly introduced grand Lorentz spaces, which allows us to derive a Hardy-Littlewood-Sobolev-type inequality. We also discuss Köthe duality for grand Lorentz spaces, from which we obtain a new Köthe dual space theorem in grand Lebesgue spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11757 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convolution-type operators in grand Lorentz spaces Nursultanov, Erlan D. Rafeiro, Humberto Suragan, Durvudkhan Functional Analysis 46E30, 46B70, 26D15 We introduce and study a novel grand Lorentz space-that we believe is appropriate for critical cases-that lies "between" the Lorentz-Karamata space and the recently defined grand Lorentz space from [1]. We prove both Young's and O'Neil's inequalities in the newly introduced grand Lorentz spaces, which allows us to derive a Hardy-Littlewood-Sobolev-type inequality. We also discuss Köthe duality for grand Lorentz spaces, from which we obtain a new Köthe dual space theorem in grand Lebesgue spaces. |
| title | Convolution-type operators in grand Lorentz spaces |
| topic | Functional Analysis 46E30, 46B70, 26D15 |
| url | https://arxiv.org/abs/2502.11757 |