Estimates for the integrals of derivatives of rational functions in multiply connecteddomains in the plane
- Authors: Baranov A.D.1, Kayumov I.R.2
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Affiliations:
- Saint Petersburg State University
- Kazan (Volga Region) Federal University
- Issue: Vol 86, No 5 (2022)
- Pages: 5-17
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/133878
- DOI: https://doi.org/10.4213/im9248
- ID: 133878
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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.
Keywords
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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