Beltrami函数的一类Hilbert边值问题

Hilbert Boundary Value Problem in Beltrami Functions

文章主要研究了上半平面内Beltrami函数的一类Hilbert边值问题。给出了Beltrami函数的一类基本解,解决了Beltrami函数的Riemann边值问题,通过把Hilbert边值问题转化为Riemann边值问题的方法,得到了上半平面内Beltrami函数的一类Hilbert边值问题的解。

This paper mainly studies on Hilbert boundary value problems in Behrami functions taken place in the upper half plane. Since a class of basic solution to Behrami function is acquired, Riemann boundary value problems in Beltrami function can be solved. By transforming Hilbert boundary value problems into Riemann ones,the solution to the former one in the upper half plane can be obtained.