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Wuhan University Journal of Natural Sciences

, Volume 3, Issue 4, pp 383–388 | Cite as

The boundedness of singular integral operator along an open curve

  • Wang Xiaolin
  • Min Honglin
Article

Abstract

It is well known that, the singular integral operatorS defined as:\(\left( {S\varphi } \right)\left( {t_0 } \right) = \frac{1}{{\pi i}}\int {_L \frac{{\varphi \left( t \right)}}{{t - t_0 }}} dt \left( {t_0 \in L} \right)\) ifL is a closed smooth contour in the complex plane C, thenS is a bounded linear operator fromH μ(L) intoH μ(L): ifL is an open smooth curve, thenS is just a linear operator fromH * intoH *. In this paper, we define a Banach space\(H_{\lambda _1 , \lambda _2 }^\mu \), and prove that\(S:H_{\lambda _1 , \lambda _2 }^\mu \to H_{\lambda _1 , \lambda _2 }^\mu \) is a bounded linear operator, then verify the boundedness of other kinds of singular integral operators.

Key words

singular integral operator \(H_{\lambda _1 , \lambda _2 }^\mu \) space boundedness 

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References

  1. 1.
    Muskhelishvili N L,Singular Integral Equations, Groningen: Noordhoff, 1962MATHGoogle Scholar
  2. 2.
    Lu Jianke.Boundary Value Problems for Analytic Functions, Singapore: World Sci, 1993Google Scholar

Copyright information

© Springer 1998

Authors and Affiliations

  • Wang Xiaolin
    • 1
  • Min Honglin
    • 1
  1. 1.College of Mathematical SciencesWuhan UniversityWuhanChina

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