Strong and Weak-Type Dispersive Estimates for the Energy-Critical Nonlinear Schrödinger Equation with an Inverse-Square Potential

We prove dispersive estimates for the three-dimensional defocusing energy-critical nonlinear Schrödinger equation associated with $\mathcal L_a=-Δ+a|x|^{-2}$. For nonnegative potentials, we extend the known finite-$p$ theory to the endpoint $L^1\to L^\infty$. For negative potentials in the global we