The Cauchy integral formula and distributional integration
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
Estrada, R. (2019). The Cauchy integral formula and distributional integration. Complex Variables and Elliptic Equations, 64 (11), 1854-1868. https://doi.org/10.1080/17476933.2018.1557159