Uniform resolvent estimates for Schrödinger operators in Aharonov-Bohm magnetic fields

We study the uniform weighted resolvent estimates of Schrödinger operator with scaling-critical electromagnetic potentials which, in particular, include the Aharonov-Bohm magnetic potential and inverse-square potential. The potentials are critical due to the scaling invariance of the model and the singularities of the potentials, which are not locally integrable. In contrast to the Laplacian −Δ on R², we prove some new uniform weighted resolvent estimates for this 2D Schrödinger operator and, as applications, we show local smoothing estimates for the Schrödinger equation in this setting.