### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

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

Research output: Contribution to journal › Article

_{b}equations',

*Communications in Partial Differential Equations*, vol. 22, no. 11-12, pp. 2061-2088.

_{b}equations. Communications in Partial Differential Equations. 1997 Dec 1;22(11-12):2061-2088.

}

TY - JOUR

T1 - Generalized Dirichlet growth theorem and applications to hypoelliptic and ∂̄b equations

AU - Arai, Hitoshi

PY - 1997/12/1

Y1 - 1997/12/1

N2 - 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).

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).

UR - http://www.scopus.com/inward/record.url?scp=0039415402&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039415402&partnerID=8YFLogxK

M3 - Article

VL - 22

SP - 2061

EP - 2088

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

SN - 0360-5302

IS - 11-12

ER -