Generalized Dirichlet growth theorem and applications to hypoelliptic and ∂̄_b equations

In this paper we give a suitable generalization of Morrey's Dirichlet growth theorem for studying higher order pseudodifferential equations on a stratified Lie group G (Theorem 1). Our generalization also improves the original one even if G is the Euclidean group. Further, we prove Morrey-Lipschitz type estimate for higher order hypoelliptic pseudodifferential equations (Theorem 3), and for the ∂̄_b equation on a strongly pseudoconvex CR manifold (Theorem 5).