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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2308.16815 |
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Table of 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.