Geodesic
On Cauchy type integrals in domains with smooth boundary
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XVI, Tome 157 (1987), pp. 173-174 Cet article a éte moissonné depuis la source Math-Net.Ru

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There exist a Jordan domain $G$ with $C^1$-boundary and a Cauchy integral $f$ in $G$ such that $(f\circ\varphi)\varphi'$ is not a Cauchy integral in the unit disc $\mathbb D$, $\varphi$ being a conformal map of $\mathbb D$ onto $G$. 
@article{ZNSL_1987_157_a17,
     author = {V. I. Morkunas},
     title = {On {Cauchy} type integrals in domains with smooth boundary},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {173--174},
     year = {1987},
     volume = {157},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_157_a17/}
}
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V. I. Morkunas. On Cauchy type integrals in domains with smooth boundary. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XVI, Tome 157 (1987), pp. 173-174. http://geodesic.mathdoc.fr/item/ZNSL_1987_157_a17/