Abstract
In this paper, we prove restriction theorems for the Fourier–Laguerre transform and establish Strichartz estimates for the Schrödinger propagator \(e^{-itL_\alpha }\) for the Laguerre operator \(L_\alpha =-\Delta -\sum _{j=1}^{n}(\dfrac{2\alpha _j+1}{x_j}\dfrac{\partial }{\partial x_j})+\dfrac{|x|^2}{4}\), \(\alpha =(\alpha _1,\alpha _2,\ldots ,\alpha _n)\in {(-\frac{1}{2},\infty )^n}\) on \(\mathbb {R}_+^n\) involving systems of orthonormal functions. The proof is based on a combination of some known dispersive estimate and the argument in Nakamura [Trans Am Math Soc 373(2), 1455–1476 (2020)] on torus. As an application, we obtain the global well-posedness for the nonlinear Laguerre–Hartree equation in Schatten space.
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Acknowledgements
The work is supported by the National Natural Science Foundation of China (Grant No. 11371036), the Natural Science Foundation of Shaanxi Province (Grant No. 2020JQ-112) and Guangdong Basic and Applied Basic Research Foundation (No. 2023A1515010656).
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Feng, G., Song, M. Restriction Theorems and Strichartz Inequalities for the Laguerre Operator Involving Orthonormal Functions. J Geom Anal 34, 287 (2024). https://doi.org/10.1007/s12220-024-01740-4
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DOI: https://doi.org/10.1007/s12220-024-01740-4