Abstract
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.
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© 1980 Springer-Verlag New York Inc.
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Rudin, W. (1980). Boundary Behavior of Cauchy Integrals. In: Function Theory in the Unit Ball of ℂn. Grundlehren der mathematischen Wissenschaften, vol 241. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8098-6_6
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DOI: https://doi.org/10.1007/978-1-4613-8098-6_6
Publisher Name: Springer, New York, NY
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