For Schrödinger operators with C^{1,1/2} potentials, the paper proves optimal commutator estimates and explicit rates for local and phase-space Weyl laws, including Hartree minimizers with Coulomb interactions.
Thanks to Lemma 3.1 and 3.2 we then get ‖ Tzγ − γ ‖ 2 L2 ≤ C HS ( |z| ‖ γ ‖ 2 L∞ + 1 |z| ‖ (TzH −H) γ ‖ 2 L∞ )
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Commutator Estimates and Quantitative Local Weyl's Law for Schr\"odinger Operators with Non-Smooth Potentials
For Schrödinger operators with C^{1,1/2} potentials, the paper proves optimal commutator estimates and explicit rates for local and phase-space Weyl laws, including Hartree minimizers with Coulomb interactions.