数学物理学报(英文版) ›› 1989, Vol. 9 ›› Issue (2): 215-226.

• 论文 • 上一篇    下一篇

SINGULAR INTEGRAL EQUATIONS IN ORLICZ SPACES (Ⅱ)

邓耀华   

  1. Institute of Computing Technology, China Academy of Bailway Sciences, Beijing, China
  • 收稿日期:1985-10-29 出版日期:1989-06-25 发布日期:1989-06-25

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

摘要: 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.

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.