∂b-方程的Cs+αp,q-形式解及其Lsp,q估计

数学季刊 ›› 2003, Vol. 18 ›› Issue (3): 234-241.

∂_b-方程的C^s+α_p,q-形式解及其L^s_p,q估计

Department of Mathematics China Coal Economic College Yantai 264005 China

收稿日期:2001-09-21 出版日期:2003-09-30 发布日期:2024-04-09
作者简介:MA Zhong-tai（1955－），male，native of Weifang，Shandong，a professor of China Coal Economic College，en- gages in boundary value problems of complex equation．
基金资助:
Supported by the Natural Science Foundation of Shandong Province（Q99A14）

C^s+α_p,q-forms Solution of ∂_b-equation and Its L^s_p,q Estimates

Department of Mathematics China Coal Economic College Yantai 264005 China

Received:2001-09-21 Online:2003-09-30 Published:2024-04-09
About author:MA Zhong-tai（1955－），male，native of Weifang，Shandong，a professor of China Coal Economic College，en- gages in boundary value problems of complex equation．
Supported by:
Supported by the Natural Science Foundation of Shandong Province（Q99A14）

摘要/Abstract

摘要： In this paper，by using holomorphic support function of strictly pseudoconvex domain on Stein manifolds and the kernel defined by DEMAILY J P and Laurent Thiebaut，we construct two integral
operators T_qand S_q which are both belong to C(∂D）and obtain integral representation of the solu-
tion of（ p q）-form ∂_b-equation on the boundary of pseudoconvex domain in Stein manifolds and the
L^s_p,q extimates for the solution .

关键词: inhomogeneous tangential Cauchy-Riemann equations, integral representation of ?b-solving,
the kernel of Demaily mand Laurent Thiebaut, Chern connection, Stein manifold,

L^s_p,q estimates

Abstract: In this paper，by using holomorphic support function of strictly pseudoconvex domain on Stein manifolds and the kernel defined by DEMAILY J P and Laurent Thiebaut，we construct two integral
operators T_qand S_q which are both belong to C(∂D）and obtain integral representation of the solu-
tion of（ p q）-form ∂_b-equation on the boundary of pseudoconvex domain in Stein manifolds and the
L^s_p,q extimates for the solution .

Key words: inhomogeneous tangential Cauchy-Riemann equations；integral representation of ?b-solving；
the kernel of Demaily mand Laurent Thiebaut；Chern connection；Stein manifold；

L^s_p,q , estimates

中图分类号:

O174．56

马忠泰. ∂_b-方程的C^s+α_p,q-形式解及其L^s_p,q估计[J]. 数学季刊, 2003, 18(3): 234-241.

MA Zhong-tai . C^s+α_p,q-forms Solution of ∂_b-equation and Its L^s_p,q Estimates [J]. Chinese Quarterly Journal of Mathematics, 2003, 18(3): 234-241.