Acta mathematica scientia,Series B ›› 1989, Vol. 9 ›› Issue (2): 215-226.

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SINGULAR INTEGRAL EQUATIONS IN ORLICZ SPACES (Ⅱ)

Deng Yaohua   

  1. Institute of Computing Technology, China Academy of Bailway Sciences, Beijing, China
  • Received:1985-10-29 Online:1989-06-25 Published:1989-06-25

Abstract: The singular integral equations with Cauchy kernels
a(t)φ(t)+b(t)/πiΓ φ(t)/(τ-t)+()(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.

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