Interpolation of classical Lorentz spaces measuring oscillation
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_ | 1866914223558230016 |
|---|---|
| author | Gogatishvili, Amiran Neves, Julio S. Pick, Luboš Turčinová, Hana |
| author_facet | Gogatishvili, Amiran Neves, Julio S. Pick, Luboš Turčinová, Hana |
| contents | We obtain an explicit characterization of the $K$-functional of a pair of weighted classical Lorentz spaces of type $S$. We develop a method for obtaining such characterization based on a relation between the desired quantity and the $K$-functional of a specific couple of spaces of type $Λ$, which are substantially more manageable than their companions of type $S$. The core of our techniques is a subtle manipulation with respective fundamental functions. We present several applications, in particular we nail down a formula for the $K$-functional of a Lebesgue space and a classical Lorentz space of type $S$ with a power weight, and using this formula we establish an inequality of a reverse Marchaud type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23287 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Interpolation of classical Lorentz spaces measuring oscillation Gogatishvili, Amiran Neves, Julio S. Pick, Luboš Turčinová, Hana Functional Analysis 46B70, 46E30, 46E35 We obtain an explicit characterization of the $K$-functional of a pair of weighted classical Lorentz spaces of type $S$. We develop a method for obtaining such characterization based on a relation between the desired quantity and the $K$-functional of a specific couple of spaces of type $Λ$, which are substantially more manageable than their companions of type $S$. The core of our techniques is a subtle manipulation with respective fundamental functions. We present several applications, in particular we nail down a formula for the $K$-functional of a Lebesgue space and a classical Lorentz space of type $S$ with a power weight, and using this formula we establish an inequality of a reverse Marchaud type. |
| title | Interpolation of classical Lorentz spaces measuring oscillation |
| topic | Functional Analysis 46B70, 46E30, 46E35 |
| url | https://arxiv.org/abs/2512.23287 |