Strichartz Estimates for the $(k,a)$-Generalized Laguerre Operators
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866915177790701568 |
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| author | Taira, Kouichi Tamori, Hiroyoshi |
| author_facet | Taira, Kouichi Tamori, Hiroyoshi |
| contents | In this paper, we prove Strichartz estimates for the $(k,a)$-generalized Laguerre operators $a^{-1}\bigl(-|x|^{2-a}Δ_k+|x|^a\bigr)$ which were introduced by Ben Sa\"ıd-Kobayashi-Orsted, and for the operators $|x|^{2-a}Δ_k$. Here $k$ denotes a non-negative multiplicity function for the Dunkl Laplacian $Δ_k$ and $a$ denotes a positive real number satisfying certain conditions. The cases $a=1,2$ were studied previously. We consider more general cases here. The proof depends on symbol-type estimates of special functions and a discrete analog of the stationary phase theorem inspired by the work of Ionescu-Jerison. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_16815 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Strichartz Estimates for the $(k,a)$-Generalized Laguerre Operators Taira, Kouichi Tamori, Hiroyoshi Analysis of PDEs Representation Theory 35Q41, 22E45 In this paper, we prove Strichartz estimates for the $(k,a)$-generalized Laguerre operators $a^{-1}\bigl(-|x|^{2-a}Δ_k+|x|^a\bigr)$ which were introduced by Ben Sa\"ıd-Kobayashi-Orsted, and for the operators $|x|^{2-a}Δ_k$. Here $k$ denotes a non-negative multiplicity function for the Dunkl Laplacian $Δ_k$ and $a$ denotes a positive real number satisfying certain conditions. The cases $a=1,2$ were studied previously. We consider more general cases here. The proof depends on symbol-type estimates of special functions and a discrete analog of the stationary phase theorem inspired by the work of Ionescu-Jerison. |
| title | Strichartz Estimates for the $(k,a)$-Generalized Laguerre Operators |
| topic | Analysis of PDEs Representation Theory 35Q41, 22E45 |
| url | https://arxiv.org/abs/2308.16815 |