中文摘要：

定义和讨论了K-解析函数在典型域S^＋={z：｜z（k）｜〈1}外的K-对称扩张函数,利用它把K-解析函数的Hilbert边值问题转化为Riemann边值问题,得到了K-解析函数类F（D（k））中Hilbert边值问题与Dirichlet边值问题的可解条件及其解的表达式.而解析函数和共轭解析函数都是K-解析函数的特例,所得结果,包含了解析函数和共轭解析函数中的相应结论.

英文摘要：

In this paper, K-symmetric extended function, a special case of K-analytic function outside of the classical domain S＋ = {z ： ｜z（k）｜ 〈 1}, is defined and studied. When it is used to convert Hilbert boundary value problem into Riemann boundary value problem, we obtain the solvable conditions and solution expression of Hilbert boundary value problem and Dirichlet boundary value problem of K-analytic function F（D（k））. As analytic functions and conjugate analytic functions are a special case of K-analytic functions, the conclusions included the corresponding results of analytic functions and conjugate analytic functions.