A remark on the Fefferman-Phong inequality for \(2\times 2\) systems
The author shows that the Fefferman-Phong inequality holds for \(2\times 2\) systems with elliptic trace provided an extra assumption is imposed on the off-diagonal terms. This condition is automatically fulfilled in the important case of off-diagonal terms that are either always real or always purely imaginary. The paper reviews the basic facts about the Weyl-Hörmander calculus. Then the theorems are stated and proved. The conditions on the off-diagonal terms are shown to be optimal by providing an example of system with positive-elliptic trace that does not satisfy either of the two conditions on hand and for which the Fefferman-Phong inequality does not hold.
scientific article; zbMATH DE number 5904816