On boundary behavior of Cauchy integrals

Hiroshige Shiga

Abstract


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.

Keywords


Cauchy integral; Plemelj-Sokthoski theorem; Riemann surface.

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References


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DOI: http://dx.doi.org/10.2478/v10062-012-0023-z
Date of publication: 2015-07-15 00:00:00
Date of submission: 2016-01-11 21:49:08


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