Strichartz Estimates for Dispersive Equations with Partial Inverse-Square Potentials

We investigate the dispersive behaviors of Schrödinger and wave equations with partial inverse-square potentials. The crucial aspect in establishing Strichartz estimates lies in constructing the spectral measure for a Schrödinger operator with partial inverse-square potentials in R2+n. This approach differs from the perturbation argument presented in Burq et al. (J Funct Anal 203:519–549, 2003) and Burq et al. (Indiana Univer Math J 53:1665–1680, 2004) because the potentials have no decay in certain directions. As applications, we prove the Strichartz estimates for Schrödinger and wave equations associated with two-particle interaction Schrödinger operators.