The Sobolev Inequalities on Real Hyperbolic Spaces and Eigenvalue Bounds for Schrödinger Operators with Complex Potentials

Xi Chen

In this paper, we prove the uniform estimates for the resolvent $(\Delta -\alpha {)}^{-1}$ as a map from $L^q$ to $L^{q^{\prime }}$ on real hyperbolic space ${\mathbb{H}}^n$ where $α\in \mathbb{C}\setminu…