Geodesic
The Norm and Regularized Trace of the Cauchy Transform
Matematičeskie zametki, Tome 77 (2005) no. 6, pp. 844-853

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In this paper, the norm of the Cauchy transform $C$ is obtained on the space $L^2(D,d\mu)$, where $d\mu=\omega(|z|)dA(z)$. Also, (for the case $\omega\equiv1$), the first regularized trace of the operator $C^*C$ on $L^2(\Omega)$ is obtained. The results are illustrated by examples, with different specific choices of the function $\omega$ and the domain $\Omega$. 
@article{MZM_2005_77_6_a3,
     author = {M. R. Dostanic},
     title = {The {Norm} and {Regularized} {Trace} of the {Cauchy} {Transform}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {844--853},
     publisher = {mathdoc},
     volume = {77},
     number = {6},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_77_6_a3/}
}
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M. R. Dostanic. The Norm and Regularized Trace of the Cauchy Transform. Matematičeskie zametki, Tome 77 (2005) no. 6, pp. 844-853. http://geodesic.mathdoc.fr/item/MZM_2005_77_6_a3/