Title

The Cauchy integral formula and distributional integration

Document Type

Article

Publication Date

1-1-2019

Abstract

We study the Cauchy representation formula for analytic functions on the unit disc whose pointwise boundary value function is distributionally integrable. We prove that the formula holds when the distributional boundary values exist, and give examples that show that it may not be true when that is not the case. We also prove a maximum principle for pointwise boundary values valid for functions with distributional boundary values.

Publication Source (Journal or Book title)

Complex Variables and Elliptic Equations

First Page

1854

Last Page

1868

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