In this paper, we shall estimate the growth order of the n-th derivative Cauchy integrals at a point in terms of the distance between the point and the boundary of the domain. By using the estimate, we shall generalize Plemelj-Sokthoski theorem. We also consider the boundary behavior of generalized Cauchy integrals on compact bordered Riemann surfaces.
@article{bwmeta1.element.doi-10_2478_v10062-012-0023-z,
author = {Hiroshige Shiga},
title = {On boundary behavior of Cauchy integrals},
journal = {Annales UMCS, Mathematica},
volume = {67},
year = {2013},
pages = {65-82},
zbl = {1284.30029},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10062-012-0023-z}
}
Hiroshige Shiga. On boundary behavior of Cauchy integrals. Annales UMCS, Mathematica, Tome 67 (2013) pp. 65-82. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10062-012-0023-z/
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