Schauder Type Estimates for a Class of Hypoelliptic Operators

The present paper aims to generalize the Schauder estimate for a class of higher-order hypo-elliptic operators. The results in the present paper apply to parabolic equations of higher order and, for example, operators like ${\mathrm{\partial }}_t^2-{\mathrm{\partial }}_x^3$. Generalization to systems is also directly obtained.