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

Hitoshi Arai

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

^*Corresponding author for this work

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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 language	English
Pages (from-to)	2061-2088
Number of pages	28
Journal	Communications in Partial Differential Equations
Volume	22
Issue number	11-12
Publication status	Published - 1997 Dec 1
Externally published	Yes

ASJC Scopus subject areas

Analysis
Applied Mathematics

Cite this

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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).",

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AB - 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).

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

Abstract

ASJC Scopus subject areas

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