Операторы постоянно й силы с оценкой снизу через производные и формал ьно гипоэллиптическ ие операторы

Abstract

For a differential operatorP(x, D) conditions are considered under which this operator has permanent strength or permanent power (in the sense of L. Hörmander) inΩ.

In the casen=2 the necessary and sufficient conditions coincide.

Using properties of permanent strength operators we get estimates of the form

$$\parallel D^v f\parallel _{L_2 } \leqq C\parallel P(x,D)f\parallel _{L_2 } (f \in C_0^\infty (\Omega ))$$

for a certain set of multiindicesν with factorС independent off∈C ^∞₀ (Ω).