The Restriction-Extension Operator on Lebesgue spaces with symmetries and applications to PDEs
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916813913194496 |
|---|---|
| author | Mandel, Rainer |
| author_facet | Mandel, Rainer |
| contents | We prove $L^p$-$L^q$-estimates for the Restriction-Extension operator acting on block-radial functions with the aid of new oscillatory integral estimates and interpolation results in mixed Lorentz spaces. Similar techniques apply to the Limiting Absorption Principles for certain elliptic (pseudo-)differential operators with constant coefficients. In this way we obtain a richer existence theory for Helmholtz-type problems on $\mathbb{R}^d$ with block-radial right hand sides. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_03020 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Restriction-Extension Operator on Lebesgue spaces with symmetries and applications to PDEs Mandel, Rainer Analysis of PDEs We prove $L^p$-$L^q$-estimates for the Restriction-Extension operator acting on block-radial functions with the aid of new oscillatory integral estimates and interpolation results in mixed Lorentz spaces. Similar techniques apply to the Limiting Absorption Principles for certain elliptic (pseudo-)differential operators with constant coefficients. In this way we obtain a richer existence theory for Helmholtz-type problems on $\mathbb{R}^d$ with block-radial right hand sides. |
| title | The Restriction-Extension Operator on Lebesgue spaces with symmetries and applications to PDEs |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2303.03020 |