Strichartz Estimates for the (, )-Generalized Laguerre Operators - Taira, Kouichi; Tamori, Hiroyoshi (Symmetry, Integrability and Geometry: Methods and Applications, 2025)
In this paper, we prove Strichartz estimates for the (, )-generalized Laguerre operators ⁻¹(−||²⁻ᵃ Δₖ + ||ᵃ) which were introduced by Ben Saïd-Kobayashi-Ørsted, and for the operators ||²⁻ᵃ Δₖ. Here k denotes a non-negative multiplicity function for the Dunkl Laplacian Δₖ, and denotes a positive real number satisfying certain conditions. The cases = 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.