Carleman inequalities and unique continuation for the polyharmonic operators

We obtain a complete characterization of Lp - Lq Carleman estimates with weight ev center dot x for the polyharmonic operators. Our result extends the Carleman inequalities for the Laplacian due to Kenig-Ruiz-Sogge. Consequently, we obtain new unique continuation properties of higher order Schrodinger equations relaxing the integrability assumption on the solution spaces.(c) 2023 Elsevier Inc. All rights reserved.