数学物理学报(英文版) ›› 2023, Vol. 43 ›› Issue (4): 1571-1586.doi: 10.1007/s10473-023-0408-9

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THE NONLINEAR BOUNDARY VALUE PROBLEM FOR k HOLOMORPHIC FUNCTIONS IN $\mathbb{C}^2$

Yanyan CUI1, Zunfeng LI2, Yonghong XIE3, Yuying QIAO3,†   

  1. 1. College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China;
    2. College of Science, Hebei University of Science and Technology, Shijiazhuang 050024, China;
    3. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, China
  • 收稿日期:2022-01-07 修回日期:2022-05-25 发布日期:2023-08-08
  • 通讯作者: †Yuying QIAO, yuyingqiao@163.com
  • 作者简介:Yanyan CUI, E-mail: cui9907081@163.com; Zunfeng LI, E-mail: zunfeng928@163.com; Yonghong XIE, E-mail: xyh1973@126.com
  • 基金资助:
    *NSF of China (11571089, 11871191), the NSF of Henan Province (222300420397), the NSF of Hebei Province (A2022208007) and the Key Foundation of Hebei Normal University (L2018Z01).

THE NONLINEAR BOUNDARY VALUE PROBLEM FOR k HOLOMORPHIC FUNCTIONS IN $\mathbb{C}^2$

Yanyan CUI1, Zunfeng LI2, Yonghong XIE3, Yuying QIAO3,†   

  1. 1. College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China;
    2. College of Science, Hebei University of Science and Technology, Shijiazhuang 050024, China;
    3. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, China
  • Received:2022-01-07 Revised:2022-05-25 Published:2023-08-08
  • Contact: †Yuying QIAO, yuyingqiao@163.com
  • About author:Yanyan CUI, E-mail: cui9907081@163.com; Zunfeng LI, E-mail: zunfeng928@163.com; Yonghong XIE, E-mail: xyh1973@126.com
  • Supported by:
    *NSF of China (11571089, 11871191), the NSF of Henan Province (222300420397), the NSF of Hebei Province (A2022208007) and the Key Foundation of Hebei Normal University (L2018Z01).

摘要: k holomorphic functions are a type of generation of holomorphic functions. In this paper, a nonlinear boundary value problem for k holomorphic functions is primarily discussed on generalized polycylinders in $\mathbb{C}^2$. The existence of the solution for the problem is studied in detail with the help of the boundary properties of Cauchy type singular integral operators with a k holomorphic kernel. Furthermore, the integral representation for the solution is obtained.

关键词: k holomorphic functions, boundary value problems, Cauchy type singular integral operators

Abstract: k holomorphic functions are a type of generation of holomorphic functions. In this paper, a nonlinear boundary value problem for k holomorphic functions is primarily discussed on generalized polycylinders in $\mathbb{C}^2$. The existence of the solution for the problem is studied in detail with the help of the boundary properties of Cauchy type singular integral operators with a k holomorphic kernel. Furthermore, the integral representation for the solution is obtained.

Key words: k holomorphic functions, boundary value problems, Cauchy type singular integral operators