The growth of hypoelliptic polynomials and Gevrey classes

Abstract:

For given hypoelliptic polynomials $P$ and $Q$, classes $\Gamma _P^\rho (\Omega )$ and $\Gamma _Q^\rho (\Omega )$ involving Gevrey type estimates on the successive iterates of the corresponding differential operators are defined. The equivalence of the inequality $|Q(\xi ){|^2} \leqq C{(1 + |P(\xi ){|^2})^h},\xi \in {R^n}$, and the inclusion $\Gamma _P^\rho (\Omega ) \subset \Gamma _Q^{\rho h}(\Omega )$ is proved.