Mathematical Sciences: Solvability and Estimates for the Tangential Cauchy-Riemann Operators

数学科学：切向柯西-黎曼算子的可解性和估计

• 批准号: 8700908
• 负责人: Mei-Chi Shaw
• 金额: $ 1.11万
• 依托单位: University of Houston
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-01 至 1987-09-01
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8700908&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Solvability; Estimates; Tangential

Work will be done on the solvability and estimates for the tangential Cauchy-Riemann operators. The global problem is an extension of earlier work on square- integrable existence and estimates for the boundary d- bar operator on weakly pseudo-convex boundaries. Efforts to obtain optimal Holder and power integral estimates, as well as the nonisotropic properties of the solutions will be done. The method proposed is to construct the integral kernels for the operator by fusing the boundary invariants and finite type conditions into the construction. Local solvability under condition Y(q) will also be studied using kernel methods. To obtain estimates for the local solution, work is planned on the analysis of singular integrals with singularities supported on a large set. Applications to problems of prescribing zeros of functions in the Nevanlinna class will be pursued. The generalized Blaschke condition must be satisfied on strongly pseudoconvex domains. The solution to this follows lines similar to the planned research on weakly pseudo-convex domains. Some related condition may provide the desired classification.

工作将在可解性和估计 切向Cauchy-Riemann算子 全球 问题是一个扩展的早期工作广场- 可积的存在性和边界D- 弱伪凸边界上的bar算子努力 为了获得最佳的保持器和功率积分估计， 以及溶液的各向异性 会完成的 所提出的方法是构造 融合边界的积分核 不变量和有限类型条件 建设 条件Y（q）下的局部可解性 也将使用核方法进行研究。 获得 当地解决方案的估计数， 奇异积分分析 在一个大的支持。 问题的应用 Nevanlinna类中函数的零点 将被追究。 广义Blaschke条件 必须满足强伪凸域。 的 解决这一问题的办法是遵循类似于计划的路线， 弱伪凸域的研究 一些相关 条件可以提供所需的分类。