四元数分析中T_Gf算子的Hlder连续性和Riemann-Hilbert边值问题 |
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引用本文: | 杨丕文.四元数分析中T_Gf算子的Hlder连续性和Riemann-Hilbert边值问题[J].数学学报,2003,46(5):993-998. |
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作者姓名: | 杨丕文 |
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作者单位: | 四川师范大学数学系,成都,610066 |
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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。
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关 键 词: | 四元数分析 T算子 Hlder连续 Riemann-Hilbert边值问题 |
文章编号: | 0583-1431(2003)05-0993-06 |
修稿时间: | 2002年1月23日 |
H(o)lder Continuity of TGf and Riemann-Hilbert Boundary Value Problem in Quaternionic Analysis |
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Institution: | Pi Wen YANG (Department of Mathematics, Sichuan Normal University, Chengdu 610066, P. R. China) |
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Abstract: | 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. |
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