Estimates for the integrals of derivatives of rational functions in multiply connecteddomains in the plane

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Abstract

We obtain estimates for the integrals of derivatives of rational functions inmultiply connected domains in the plane.A sharp order of growth is found for the integral of the modulus of thederivative of a finite Blaschke product in the unit disc.We also extend the results of Dolzhenko about the integrals of thederivatives of rational functions to a wider class of domains, namely, todomains bounded by rectifiable curves without zero interior angles, and showthe sharpness of the results obtained.

About the authors

Anton Dmitrievich Baranov

Saint Petersburg State University

Email: anton.d.baranov@gmail.com
Doctor of physico-mathematical sciences, Associate professor

Ilgiz Rifatovich Kayumov

Kazan (Volga Region) Federal University

Email: Ilgis.Kayumov@kpfu.ru
Doctor of physico-mathematical sciences, Head Scientist Researcher

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Copyright (c) 2022 Baranov A.D., Kayumov I.R.

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