四元数分析中T_Gf算子的Hlder连续性和Riemann-Hilbert边值问题  

Hlder Continuity of TG f and Riemanu-Hilbert Boundary Value Problem in Quaternionic Analysis

作　　者：杨丕文[1] 

机构地区：[1]四川师范大学数学系,成都610066

出　　处：《数学学报（中文版）》2003年第5期993-998,共6页Acta Mathematica Sinica：Chinese Series

摘　　要：本文证明了四元数分析中的有界区域G上的非齐次Dirac方程u=f的分布解T_Gf,当f∈L_P(G),P>4时,在G上具有Holder连续性,讨论了超球和双圆柱上的方程u=f的Riemann-Hilbert边值问题,给出了可解条件和通解的积分表示,并且还证明了通解的Holder连续性。In this paper, it is shown that if f∈ LP(G), P > 4, the distribution solution Tcf of the inhomogeneous Dirac equation u= f on a bounded domain G in quaternionic analysis is Holder continuous on G. The Riemann-Hilbert boundary value problems for the equation u = f on the ball and bicylinder are investigated. The solvable conditions and the integral expressions of the general solution are given, and the Holder continuity of the general solutions is proved.

关 键 词：四元数分析 T算子 HOELDER连续 RIEMANN-HILBERT边值问题 

分 类 号：O175.25[理学—数学] O175.8[理学—基础数学]