\(L^ p\)-estimates for Schrödinger operators
Operators \(H = - \Delta + V\) on \(\mathbb{R}^d\) with real-valued potential \(V = V_+ - V_-\) are considered, where \(V_\pm \geq 0\), \(V_+ \in L^1_{\text{loc}} (\mathbb{R}^d)\) and \(V_- \in K_d\) where \(K_d\) is the Kato class. Estimates for the resolvent of the operators in \(L^p (\mathbb{R}^d)\) are proved. One of these estimates is \[ \bigl |(H - z)^{-1} \bigr |\leq C_{p,R} \text{dist} \bigl( z, \sigma (H) \bigr)^{- \beta - 1} \] for any \(1 \leq p < \infty\), \(|z |\leq R\) where \(\beta = d |1/2 - 1/p |\).
scientific article; zbMATH DE number 729851