### Abstract

An integral kernel approach is given for the proof of the theorem of Andreotti and Hill which states that the Y(_{q}) condition of Kohn is a sufficient condition for local solvability of the tangential Cauchy Riemann equations on a real hypersurface in C". In addition, we provide an integral kernel approach to nonsolvability for a certain class of real hypersurfaces in the case when Y(_{q}) is not satisfied.

Original language | English (US) |
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Pages (from-to) | 643-658 |

Number of pages | 16 |

Journal | Transactions of the American Mathematical Society |

Volume | 289 |

Issue number | 2 |

DOIs | |

State | Published - 1985 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**A kernel approach to the local solvability of the tangential cauchy riemann equations.** / Boggess, Albert; Shaw, M. C.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 289, no. 2, pp. 643-658. https://doi.org/10.1090/S0002-9947-1985-0784007-7

}

TY - JOUR

T1 - A kernel approach to the local solvability of the tangential cauchy riemann equations

AU - Boggess, Albert

AU - Shaw, M. C.

PY - 1985

Y1 - 1985

N2 - An integral kernel approach is given for the proof of the theorem of Andreotti and Hill which states that the Y(q) condition of Kohn is a sufficient condition for local solvability of the tangential Cauchy Riemann equations on a real hypersurface in C". In addition, we provide an integral kernel approach to nonsolvability for a certain class of real hypersurfaces in the case when Y(q) is not satisfied.

AB - An integral kernel approach is given for the proof of the theorem of Andreotti and Hill which states that the Y(q) condition of Kohn is a sufficient condition for local solvability of the tangential Cauchy Riemann equations on a real hypersurface in C". In addition, we provide an integral kernel approach to nonsolvability for a certain class of real hypersurfaces in the case when Y(q) is not satisfied.

UR - http://www.scopus.com/inward/record.url?scp=0041038321&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041038321&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1985-0784007-7

DO - 10.1090/S0002-9947-1985-0784007-7

M3 - Article

VL - 289

SP - 643

EP - 658

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 2

ER -