## Abstract

Let Ω be an open, relatively compact subset in C^{n+1}, and assume the boundary of Ω, ∂Ω, is smooth and strongly pseudoconvex. Let Op(K) be an integral operator with mixed type homogeneities defined on Ω: i.e., K has the form as follows: where E_{k}is a homogeneous kernel of degree -K: in the Euclidean sense and H_{1}is homogeneous of degree -1 in the Heisenberg sense. In this paper, we study the optimal U and Holder estimates for the kernel K. We also use Lieb- Range's method to construct the integral kernel for the Kohn solution ∂N of the Cauchy-Riemann equation on the Siegel upper-half space and then apply our results to ∂N. On the other hand, we prove Lieb-Range's kernel gains 1 in "good" directions (hence gains 1/2 in all directions) via Phong-Stein's theory. We also discuss the transferred kernel from the Siegel upper-half space to fi.

Original language | English (US) |
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Pages (from-to) | 273-304 |

Number of pages | 32 |

Journal | Transactions of the American Mathematical Society |

Volume | 315 |

Issue number | 1 |

DOIs | |

State | Published - Sep 1989 |

Externally published | Yes |

## ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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