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