Boundary Behavior of Cauchy Integrals
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.
KeywordsLipschitz Function Toeplitz Operator Boundary Behavior Cauchy Kernel Cauchy Formula
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