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

For s > 0, let H-0 = (-Delta)(s) be the fractional Laplacian. In this paper, we obtain Lieb-Thirring type inequalities for the fractional Schrodinger operator defined as H = H-0 + V, where V is an element of L-P(R-d),p >= 1, d >= 1, is a complex-valued potential. Our methods are based on the results of articles by Borichev-Golinskii-Kupin [BGKO9] and Hansmann [Han 11].