# On boundary behavior of Cauchy integrals

Annales UMCS, Mathematica (2013)

- Volume: 67, Issue: 1, page 65-82
- ISSN: 2083-7402

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topHiroshige Shiga. "On boundary behavior of Cauchy integrals." Annales UMCS, Mathematica 67.1 (2013): 65-82. <http://eudml.org/doc/268084>.

@article{HiroshigeShiga2013,

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.},

author = {Hiroshige Shiga},

journal = {Annales UMCS, Mathematica},

keywords = {Cauchy integral; Plemelj-Sokthoski theorem; Riemann surface; Plemelj-Sokhotski theorem},

language = {eng},

number = {1},

pages = {65-82},

title = {On boundary behavior of Cauchy integrals},

url = {http://eudml.org/doc/268084},

volume = {67},

year = {2013},

}

TY - JOUR

AU - Hiroshige Shiga

TI - On boundary behavior of Cauchy integrals

JO - Annales UMCS, Mathematica

PY - 2013

VL - 67

IS - 1

SP - 65

EP - 82

AB - 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.

LA - eng

KW - Cauchy integral; Plemelj-Sokthoski theorem; Riemann surface; Plemelj-Sokhotski theorem

UR - http://eudml.org/doc/268084

ER -

## References

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- [9] Guseinov, E. G., The Plemelj-Privalov theorem for generalized H¨older classes, Mat. Sb. 183, no. 2 (1992), 21-37 (Russian); translation in Russian Acad. Sci. Sb. Math. 75 (1993), 165-182.
- [10] Heins, M., Hardy Classes on Riemann Surfaces, Springer-Verlag, Berlin-New York, 1969. Zbl0176.03001
- [11] Shiga, H., Riemann mappings of invariant components of Kleinian groups, J. London Math. Soc. 80 (2009), 716-728. Zbl1184.30036
- [12] Shiga, H., Modulus of continuity, a Hardy-Littlewood theorem and its application, RIMS Kokyuroku Bessatsu, 2010, 127-133. Zbl1220.30058
- [13] Pommerenke, C., Boundary Behaviour of Conformal Maps, Springer-Verlag, Berlin, 1992. Zbl0762.30001
- [14] Walsh, J. L., Polynomial expansions of functions defined by Cauchy’s integral, J. Math. Pures Appl. 31 (1952), 221-244. Zbl0049.05203

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