Estimates for integrals of derivatives of rational functions in multiply connected domains in the plane

A. D. Baranov; I. R. Kayumov

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arXiv · 2112.01391

Estimates for integrals of derivatives of rational functions in multiply connected domains in the plane

A. D. Baranov·I. R. Kayumov

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Abstract

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

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BibTeX RIS

A. D. Baranov, I. R. Kayumov. 2021-12-02. Estimates for integrals of derivatives of rational functions in multiply connected domains in the plane. https://arxiv.org/abs/2112.01391

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