数学物理学报(英文版) ›› 1989, Vol. 9 ›› Issue (2): 215-226.
邓耀华
Deng Yaohua
摘要: The singular integral equations with Cauchy kernels
a(t)φ(t)+b(t)/πi∫Γ φ(t)/(τ-t)dτ+(Tφ)(t)=f(t)
have studied in Lp(Γ),∀p > 1,in detail.Here Γ stands for the set of a finite number of closed Liapunoff's curves which have no common points and T denotes the completely continuous operator in the space sunder consideration. In this paper, we consider the equations mentioned above in Orlicz spaces LM(Γ). It is proved that the Nether theorem and the index formula are hold true in the case of reflexive Orlicz spaces.