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

Research output: Contribution to journalArticle

Abstract

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).

Original languageEnglish
Pages (from-to)2061-2088
Number of pages28
JournalCommunications in Partial Differential Equations
Volume22
Issue number11-12
Publication statusPublished - 1997 Dec 1
Externally publishedYes

Fingerprint

Lie groups
Dirichlet
Theorem
Higher Order
CR Manifold
Pseudoconvex
Lipschitz
Euclidean
Estimate
Generalization

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Generalized Dirichlet growth theorem and applications to hypoelliptic and ∂̄b equations. / Arai, Hitoshi.

In: Communications in Partial Differential Equations, Vol. 22, No. 11-12, 01.12.1997, p. 2061-2088.

Research output: Contribution to journalArticle

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