Boundary Behavior of Cauchy Integrals

  • Walter Rudin
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 241)


One major difference between the Poisson kernel and the Cauchy kernel is that the former is positive and the latter is not. The positivity of P(z, ζ) made it possible to be rather unsubtle in the proof of the basic maximal theorem 5.4.5: μ was replaced ∣μ∣ and it was then just a matter of making size estimates without giving too much away. No cancellation effects came into play.


Lipschitz Function Toeplitz Operator Boundary Behavior Cauchy Kernel Cauchy Formula 
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Copyright information

© Springer-Verlag New York Inc. 1980

Authors and Affiliations

  • Walter Rudin
    • 1
  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA

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