Acta mathematica scientia,Series B ›› 2024, Vol. 44 ›› Issue (5): 1837-1852.doi: 10.1007/s10473-024-0511-6

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BOUNDARY VALUE PROBLEMS OF CONJUGATE AND GENERALIZED $k$-HOLOMORPHIC FUNCTIONS IN $\mathbb{C}^2$*

Yanyan CUI1, Chaojun WANG1, Yonghong XIE2, Yuying QIAO2,†   

  1. 1. College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China;
    2. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, China
  • Received:2023-02-08 Revised:2024-05-30 Online:2024-10-25 Published:2024-10-22
  • Contact: †Yuying QIAO, E-mail,: yuyingqiao@163.com
  • About author:Yanyan CUI,E-mail,: cui9907081@163.com; Chaojun WANG,E-mail,: wang9907081@163.com; Yonghong XIE,E-mail,: xyh1973@126.com
  • Supported by:
    Cui's research was supported by the NSF of Henan Province (222300420397, 242300421394), Xie's research was supported by the NSFC (11571089, 11871191).

Abstract: In this paper, conjugate $k$-holomorphic functions and generalized $k$-holomorphic functions are defined in the two-dimensional complex space, and the corresponding Riemann boundary value problems and the inverse problems are discussed on generalized bicylinders. By the characteristics of the corresponding functions and boundary properties of the Cauchy type singular integral operators with conjugate $k$-holomorphic kernels, the general solutions and special solutions of the corresponding boundary value problems are studied in a detailed fashion, and the integral expressions of the solutions are obtained.

Key words: several complex variables, $k$-holomorphic functions, partial difference equations, polyanalytic functions

CLC Number: 

  • 32A30
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