Note on Lieb-Thirring Type Inequalities for a Complex Perturbation of Fractional Laplacian

摘要

For s > 0, let H ₀ = (-?) ^s be the fractional Laplacian. In this paper, we obtain Lieb-Thirring type inequalities for the fractional Schr?dinger operator defined as H = H ₀ + V , where V ∈ L^p (? ^d ), p ≥ 1, d ≥ 1, is a complex-valued potential. Our methods are based on the results of articles by Borichev-Golinskii-Kupin [BGK09] and Hansmann [Han11].