Strichartz Estimates for the (𝑘, 𝑎)-Generalized Laguerre Operators

Abstract

In this paper, we prove Strichartz estimates for the (𝑘, 𝑎)-generalized Laguerre operators 𝑎⁻¹(−|𝑥|²⁻ᵃ Δₖ + |𝑥|ᵃ) which were introduced by Ben Saïd-Kobayashi-Ørsted, and for the operators |𝑥|²⁻ᵃ Δₖ. Here k denotes a non-negative multiplicity function for the Dunkl Laplacian Δₖ, 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.